H=2.403 L+23.31 A group of biology students conducted an experiment to study the relationship between a person's femur length and the person's height. The given equation describes the relationship between the length L, in inches, of a student's femur and the student's estimated height H, in inches, for the students in the group. Which of the following is the best interpretation of 2.403 in this context?

A. The increase in a student's estimated height, in inches, for each increase of 1 inch in the student's femur length.

B. The increase in a student's femur length, in inches, for each increase of 1 inch in the student's estimated height.

C. The increase in a student's femur length, in inches, for each increase of 23.31 inches in the student's estimated height.

D. The estimated height, in inches, of a student whose femur has a length of L inches.

y -4 x-9 For which of the following tables are all the values of x and their corresponding values of y solutions to the given system of inequalities?

D. {cc} x & y -5 & 13 -6 & 17 -8 & 25

A. {cc} x & y -5 & 9 -6 & 25 -8 & -6

B. {cc} x & y -5 & 10 -6 & 18 -8 & 30

C. {cc} x & y -5 & 12 -6 & 20 -8 & 31

y>5 x-4 For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?

C. {cc} x & y 4 & 21 6 & 31 9 & 46

A. {cc} x & y 4 & 11 6 & 21 9 & 36

B. {cc} x & y 4 & 16 6 & 26 9 & 41

D. {cc} x & y 4 & 21 6 & 21 9 & 41

In one week in 2017, a technician earned a total of \700 by working at her regular job and at a second job doing part-time work. The equation 16 h+13 c=700 represents this situation, where h is the number of hours worked at her regular job and c is the number of hours worked at her second job. Which of the following is the best interpretation of 16 in this context?

A. The amount, in dollars, the technician earned for each hour she worked at her regular job

B. The amount, in dollars, the technician earned for each hour she worked at her second job

C. The number of hours the technician worked in one week at her regular job

D. The number of hours the technician worked in one week at her second job

y > - {7}{2}x + 17 For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?

A. {cc} x & y -2 & 26 2 & 12 4 & 5

B. {cc} x & y -2 & 26 2 & 8 4 & 5

C. {cc} x & y -2 & 22 2 & 8 4 & 1

D. {cc} x & y -2 & 24 2 & 12 4 & 5

SAT Algebra Practice Questions

Algebra is the largest math domain on the digital SAT: roughly 13 to 15 of the 44 math questions, about 35% of your math score. It covers linear equations in one and two variables, systems of two linear equations, linear inequalities, and linear functions.

Most lost points here are not from hard concepts. They come from rushing the translation step (turning a word problem into an equation), sign slips when isolating a variable, and misreading which quantity a coefficient represents. The questions below are drawn from our bank of 4,100+ and mirror the real test's range: work each one before opening the explanation.

Question 1Linear equations in one variable · easy
$H=2.403 L+23.31$

A group of biology students conducted an experiment to study the relationship between a person's femur length and the person's height. The given equation describes the relationship between the length $L$ , in inches, of a student's femur and the student's estimated height $H$ , in inches, for the students in the group. Which of the following is the best interpretation of 2.403 in this context?
AThe increase in a student's estimated height, in inches, for each increase of 1 inch in the student's femur length.
BThe increase in a student's femur length, in inches, for each increase of 1 inch in the student's estimated height.
CThe increase in a student's femur length, in inches, for each increase of 23.31 inches in the student's estimated height.
DThe estimated height, in inches, of a student whose femur has a length of $L$ inches.
Show answer & explanation
Correct answer: A
The increase in a student's estimated height, in inches, for each increase of 1 inch in the student's femur length.
Option A is correct

The equation $H = 2.403L + 23.31$ has the form $H = mL + b$ , so 2.403 is the slope: the change in $H$ produced by increasing $L$ by exactly 1.

$L$ is femur length in inches and $H$ is estimated height in inches. So each additional inch of femur length adds 2.403 inches to the estimated height.

Choice B reverses the relationship — that would describe the slope if the equation were solved for $L$ instead. Choice D describes what the whole expression $2.403L + 23.31$ computes, not what the single number 2.403 means.

Answer: A.
Option B is incorrect
This reverses the relationship. 2.403 multiplies the femur length $L$ , so it converts femur inches into height inches. The rate of femur change per inch of height would come from solving the equation for $L$ , which gives a slope of $\tfrac{1}{2.403} \approx 0.416$ , not 2.403.
Option C is incorrect
This mixes the intercept into the rate. 23.31 is the constant term — the height estimate when $L = 0$ — and it plays no role in how much $H$ changes per inch of femur. There is no "23.31-inch step" anywhere in the equation.
Option D is incorrect
This describes the output of the whole expression $2.403L + 23.31$ , which is the estimated height $H$ . The question asks about the single number 2.403, and a coefficient is a rate of change, not a height.
Question 2Systems of two linear equations in two variables · medium
$\begin{gathered} y<-6 x-16 \\ y>-4 x-9 \end{gathered}$
For which of the following tables are all the values of $x$ and their corresponding values of $y$ solutions to the given system of inequalities?
A $\begin{array}{|c|c|} \hline x & y \\ \hline -5 & 9 \\ \hline -6 & 25 \\ \hline -8 & -6 \\\hline \end{array}$
B $\begin{array}{|c|c|} \hline x & y \\ \hline -5 & 10 \\ \hline -6 & 18 \\ \hline -8 & 30 \\\hline \end{array}$
C $\begin{array}{|c|c|} \hline x & y \\ \hline -5 & 12 \\ \hline -6 & 20 \\ \hline -8 & 31 \\\hline \end{array}$
D $\begin{array}{|c|c|} \hline x & y \\ \hline -5 & 13 \\ \hline -6 & 17 \\ \hline -8 & 25 \\\hline \end{array}$
Show answer & explanation
Correct answer: D
Option A is incorrect
The first row already fails. At $x = -5$ , the second inequality requires $y > -4(-5) - 9 = 11$ , but this table gives $y = 9$ , and $9 > 11$ is false.
Option B is incorrect
The first row fails the same test. At $x = -5$ , $y$ must be greater than 11, but this table gives $y = 10$ .
Option C is incorrect
The middle row sits on a boundary. At $x = -6$ , the first inequality requires $y < -6(-6) - 16 = 20$ strictly, but this table gives $y = 20$ — on the line is not inside the region.
Option D is correct

A table works only if every row satisfies both inequalities, so test rows and eliminate on the first failure.

All four tables use $x = -5, -6, -8$ . Compute both boundaries once: at $x=-5$ , $-6x-16 = 14$ and $-4x-9 = 11$ , so $y$ must satisfy $11 < y < 14$ . At $x=-6$ : 20 and 15, so $15 < y < 20$ . At $x=-8$ : 32 and 23, so $23 < y < 32$ .

Choice A gives $y=9$ at $x=-5$ , but $9 < 11$ — fails. Choice B gives $y=10$ — also below 11. Choice C gives $y=20$ at $x=-6$ , but $y < 20$ must be strict — fails.

Choice D gives 13, 17, 25, which land inside $(11,14)$ , $(15,20)$ , and $(23,32)$ respectively.

Answer: D.
Question 3Linear inequalities in one or two variables · easy
$y>5 x-4$

For which of the following tables are all the values of x and their corresponding values of $y$ solutions to the given inequality?
A $\begin{array}{|c|c|} \hline x & y \\ \hline 4 & 11 \\ \hline 6 & 21 \\ \hline 9 & 36 \\\hline \end{array}$
B $\begin{array}{|c|c|} \hline x & y \\ \hline 4 & 16 \\ \hline 6 & 26 \\ \hline 9 & 41 \\\hline \end{array}$
C $\begin{array}{|c|c|} \hline x & y \\ \hline 4 & 21 \\ \hline 6 & 31 \\ \hline 9 & 46 \\\hline \end{array}$
D $\begin{array}{|c|c|} \hline x & y \\ \hline 4 & 21 \\ \hline 6 & 21 \\ \hline 9 & 41 \\\hline \end{array}$
Show answer & explanation
Correct answer: C
Option A is incorrect
The first row fails: at $x = 4$ the boundary is $5(4) - 4 = 16$ , and this table's $y = 11$ is below it, not above.
Option B is incorrect
At $x = 4$ this table gives $y = 16$ , which equals the boundary exactly. The inequality is strict ( $>$ ), so a point on the line $y = 5x - 4$ is not a solution.
Option C is correct

For each $x$ in the tables, compute the boundary $5x - 4$ ; a valid row needs $y$ strictly greater than it.

At $x = 4$ : $5(4)-4 = 16$ . At $x = 6$ : 26. At $x = 9$ : 41.

Choice A starts with $y = 11$ at $x=4$ , and $11 < 16$ — fails immediately. Choice B gives $y = 16$ at $x=4$ , but the inequality is strict, so $y = 16$ is on the line, not above it — fails. Choice D gives $y = 21$ at $x = 6$ , but $21 < 26$ — fails.

Choice C gives $21 > 16$ , $31 > 26$ , and $46 > 41$ : every row clears its boundary.

Answer: C.
Option D is incorrect
The middle row fails: at $x = 6$ the boundary is $5(6) - 4 = 26$ , and this table's $y = 21$ is below it.
Question 4Linear Functions · hard
A polygonal chain is a connected series of line segments whose length is defined as the sum of the lengths of the line segments it is made of. A polygonal chain with a length of 33 centimeters (cm) is extended by adding line segments that each have a length of $8 - r$ cm. Which function $f$ represents the total length, in cm, of the extended polygonal chain after $x$ line segments are added?
A $f(x) = 33(8 - r) + x$
B $f(x) = 8x - rx + 33$
C $f(x) = 8x - r + 33$
D $f(x) = (41 - r)x$
Show answer & explanation
Correct answer: B
$f(x) = 8x - rx + 33$
Option A is incorrect
This multiplies the starting length 33 by $(8 - r)$ , rescaling the original chain. The original 33 cm does not change when segments are added — it must appear as a plain constant.
Option B is correct

The chain starts at 33 cm, and that fixed starting length does not change as segments are added — it is the constant term.

Each added segment contributes $(8 - r)$ cm, so adding $x$ segments contributes $(8-r)x$ cm in total.

Total length: $f(x) = 33 + (8 - r)x$ . Distribute: $f(x) = 8x - rx + 33$ .

Choice A multiplies the starting length by $(8-r)$ , which wrongly rescales the original chain. Choice C forgets to multiply $r$ by $x$ , subtracting $r$ only once no matter how many segments are added.

Answer: B.
Option C is incorrect
This subtracts $r$ only once, no matter how many segments are added. Each of the $x$ segments is $(8 - r)$ cm, so the $r$ must be multiplied by $x$ too: $(8 - r)x = 8x - rx$ .
Option D is incorrect
This has no constant term, so the chain would start at length 0 instead of 33. The 41 comes from wrongly adding $33 + 8$ , which merges a fixed length with a per-segment rate.
Question 5Linear equations in one variable · medium
In one week in 2017, a technician earned a total of $700 by working at her regular job and at a second job doing part-time work. The equation $16 h+13 c=700$ represents this situation, where $h$ is the number of hours worked at her regular job and $c$ is the number of hours worked at her second job. Which of the following is the best interpretation of 16 in this context?
AThe amount, in dollars, the technician earned for each hour she worked at her regular job
BThe amount, in dollars, the technician earned for each hour she worked at her second job
CThe number of hours the technician worked in one week at her regular job
DThe number of hours the technician worked in one week at her second job
Show answer & explanation
Correct answer: A
The amount, in dollars, the technician earned for each hour she worked at her regular job
Option A is correct

In $16h + 13c = 700$ , the term $16h$ must be an amount of money, because it adds with $13c$ to make 700$.

Since $h$ counts hours at the regular job, multiplying it by 16 turns hours into dollars only if 16 is the pay rate, in dollars per hour, at the regular job.

Choice B attaches the rate to the wrong job — the second job's rate is 13, the coefficient of $c$ . Choices C and D confuse a rate (a coefficient) with a quantity of hours (a variable): the number of hours worked is $h$ or $c$ , not 16.

Answer: A.
Option B is incorrect
The second job's pay rate is the coefficient of $c$ , which is 13 — since $c$ counts hours at the second job. 16 goes with $h$ , the regular job.
Option C is incorrect
16 is a coefficient, a rate in dollars per hour — not a count of hours. The number of hours at the regular job is the variable $h$ itself.
Option D is incorrect
Same confusion with the other variable: hours at the second job is $c$ , and 16 is not a number of hours at all but the regular job's hourly pay.
Question 6Systems of two linear equations in two variables · easy
$\begin{gathered} y>-5 x-21 \\ y>-3 x-8 \end{gathered}$
For which of the following tables are all the values of $x$ and their corresponding values of $y$ solutions to the given system of inequalities?
A $(-8,14),(-9,35),(-11,3)$
B $(-8,19),(-9,22),(-11,-3)$
C $(14,-8),(35,-9),(3,-11)$
D $(19,-8),(22,-9),(-3,-11)$
Show answer & explanation
Correct answer: C
$(14,-8),(35,-9),(3,-11)$
Option A is incorrect
These are choice C's numbers with the coordinates swapped. Taking $(x, y) = (-8, 14)$ : the first inequality requires $y > -5(-8) - 21 = 19$ , and $14 > 19$ is false.
Option B is incorrect
The first pair $(-8, 19)$ lands exactly on the first boundary: $y$ must be strictly greater than 19, and $19 > 19$ is false.
Option C is correct

Each option lists ordered pairs $(x, y)$ — and the trap here is that choices A and B use the same numbers as C and D with the coordinates swapped, so keep the order straight.

Test choice C. For $(14, -8)$ : $-5(14)-21 = -91$ and $-3(14)-8 = -50$ ; -8 is greater than both. For $(35, -9)$ : boundaries -196 and -113; -9 beats both. For $(3, -11)$ : boundaries -36 and -17; -11 beats both. Every pair works.

Why the others fail: choice A's first pair $(-8, 14)$ gives $-5(-8)-21 = 19$ , and $14 > 19$ is false. Choice B's first pair $(-8, 19)$ gives $19 > 19$ , false because the inequality is strict. Choice D's pair $(-3, -11)$ gives $-5(-3)-21 = -6$ , and $-11 > -6$ is false.

Answer: C.
Option D is incorrect
The last pair fails: at $(x, y) = (-3, -11)$ , the first inequality requires $y > -5(-3) - 21 = -6$ , and $-11 > -6$ is false.
Question 7Linear inequalities in one or two variables · easy
$y > -\frac{7}{2}x + 17$

For which of the following tables are all the values of $x$ and their corresponding values of $y$ solutions to the given inequality?
A $\begin{array}{|c|c|} \hline x & y \\ \hline -2 & 26 \\ \hline 2 & 12 \\ \hline 4 & 5 \\\hline \end{array}$
B $\begin{array}{|c|c|} \hline x & y \\ \hline -2 & 26 \\ \hline 2 & 8 \\ \hline 4 & 5 \\\hline \end{array}$
C $\begin{array}{|c|c|} \hline x & y \\ \hline -2 & 22 \\ \hline 2 & 8 \\ \hline 4 & 1 \\\hline \end{array}$
D $\begin{array}{|c|c|} \hline x & y \\ \hline -2 & 24 \\ \hline 2 & 12 \\ \hline 4 & 5 \\\hline \end{array}$
Show answer & explanation
Correct answer: A
Option A is correct

Compute the boundary $-\tfrac{7}{2}x + 17$ for the three $x$ -values every table uses.

At $x = -2$ : $7 + 17 = 24$ . At $x = 2$ : $-7 + 17 = 10$ . At $x = 4$ : $-14 + 17 = 3$ .

A valid table needs $y$ strictly above the boundary in every row. Choice B fails at $x=2$ ( $8 < 10$ ). Choice C fails at $x=-2$ ( $22 < 24$ ). Choice D fails at $x=-2$ : $y = 24$ equals the boundary, and equality is not allowed by a strict inequality.

Choice A gives $26 > 24$ , $12 > 10$ , and $5 > 3$ — all three rows clear.

Answer: A.
Option B is incorrect
The middle row fails: at $x = 2$ the boundary is $-\tfrac{7}{2}(2) + 17 = 10$ , and this table's $y = 8$ is below it.
Option C is incorrect
The first row fails: at $x = -2$ the boundary is $7 + 17 = 24$ , and $22 < 24$ .
Option D is incorrect
At $x = -2$ this table gives exactly 24, the boundary value. The inequality is strict, so a point on the line itself is not a solution.
Question 8Linear Functions · easy
A linear function $f$ gives a company’s profit, in dollars, for selling $x$ items. The company’s profit is $190 when it sells 4 items, and its profit is $670 when it sells 10 items. Which equation defines $f$ ?
A $f(x) = 180x - 670$
B $f(x) = 67x$
C $f(x) = 80x - 10x$
D $f(x) = 80x - 130$
Show answer & explanation
Correct answer: D
$f(x) = 80x - 130$
Option A is incorrect
This mashes the given numbers into the wrong slots. Check with the known point: $f(4) = 180(4) - 670 = 50$ , not 190.
Option B is incorrect
This forces the line through the origin (zero profit at zero items, no fixed costs), which contradicts the data: $f(4) = 67(4) = 268$ , not 190.
Option C is incorrect
$80x - 10x$ simplifies to $70x$ — it looks like it uses the right slope but doesn't. Check: $f(4) = 280$ , not 190.
Option D is correct

A linear function through the points $(4, 190)$ and $(10, 670)$ has slope $\dfrac{670 - 190}{10 - 4} = \dfrac{480}{6} = 80$ — the company earns 80$ more per extra item.

Write $f(x) = 80x + b$ and substitute $(4, 190)$ : $190 = 320 + b$ , so $b = -130$ .

So $f(x) = 80x - 130$ . Check with the second point: $80(10) - 130 = 670$ . ✓

Choice C looks plausible but simplifies to $70x$ , which gives $f(4) = 280$ , not 190. Choice B forces the line through the origin, which contradicts both given points.

Answer: D.
Question 9Systems of two linear equations in two variables · medium
A biologist is designing a study to observe the behavior of male and female amethyst-throated hummingbirds. According to the study's design, at least 91 hummingbirds will be observed, and the positive difference between the number of males, $x$ , and the number of females, $y$ , will not exceed 8. Which of the following systems of inequalities represents this situation?
A $x+y \geq 91$ $|x-y| \leq 8$
B $x+y \geq 91$ $x-y \leq 8$
C $x+y \leq 91$ $x-y \leq 8$
D $x+y < 91$ $|x-y| < 8$
Show answer & explanation
Correct answer: A
$x+y \geq 91$ $|x-y| \leq 8$
Option A is correct

"At least 91 hummingbirds will be observed" means the total is 91 or more: $x + y \geq 91$ . That eliminates choices C and D, which cap the total instead.

"The positive difference between the number of males and females will not exceed 8" must hold whichever group is larger. If females outnumber males, $x - y$ is negative and choice B's $x - y \leq 8$ would be satisfied even with a difference of 50.

The absolute value captures both directions: $|x - y| \leq 8$ says the gap is at most 8 regardless of which count is bigger.

Answer: A.
Option B is incorrect
$x - y \leq 8$ only bounds the difference in one direction. If females outnumber males by, say, 50, then $x - y = -50 \leq 8$ is satisfied — but the study's rule is violated. The absolute value is what catches both directions.
Option C is incorrect
$x + y \leq 91$ caps the total at 91, but "at least 91 hummingbirds" means the total must be 91 or more: $x + y \geq 91$ .
Option D is incorrect
Both inequalities are strict here, but the study allows exactly 91 birds ("at least 91") and a difference of exactly 8 ("will not exceed 8"), so both must be inclusive: $\geq$ and $\leq$ .
Question 10Linear Functions · medium
A landscaping company mixes oil with gasoline to power its tools. A chainsaw requires 8 ounces of oil per gallon of gasoline. A lawnmower requires 4 ounces of oil per gallon of gasoline. The company uses a total of 21 ounces of oil in its mixes for the chainsaw and lawnmower. Which of the following equations represents this situation, where $x$ represents the amount of gasoline, in gallons, in the mix for the chainsaw and $y$ represents the amount of gasoline, in gallons, in the mix for the lawnmower?
A $2(x + 2y) = 21$
B $2(2x + y) = 21$
C $4(x + 2y) = 21$
D $4(2x + y) = 21$
Show answer & explanation
Correct answer: D
$4(2x + y) = 21$
Option A is incorrect
Expanding gives $2x + 4y = 21$ : the chainsaw would use 2 ounces per gallon instead of 8. The chainsaw's mix is the heavier one.
Option B is incorrect
Expanding gives $4x + 2y = 21$ : the chainsaw at 4 and the lawnmower at 2 ounces per gallon — both rates are half of what the problem states.
Option C is incorrect
Expanding gives $4x + 8y = 21$ : this attaches 8 ounces per gallon to the lawnmower and 4 to the chainsaw — the two tools' oil rates are swapped.
Option D is correct

Translate each mix into ounces of oil. The chainsaw uses 8 ounces per gallon and gets $x$ gallons: $8x$ ounces. The lawnmower uses 4 ounces per gallon and gets $y$ gallons: $4y$ ounces.

The total oil used is 21 ounces: $8x + 4y = 21$ .

No choice is written in that form, so factor. The greatest common factor of 8 and 4 is 4: $8x + 4y = 4(2x + y)$ , giving $4(2x + y) = 21$ .

Expanding the wrong choices exposes them: choice A is $2x + 4y = 21$ and choice C is $4x + 8y = 21$ — both attach the oil rates to the wrong tools.

Answer: D.

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