If x + y = 10 and x - y = 4, what is the value of y?

A. 3. Subtract the second equation from the first: (x + y) - (x - y) = 10 - 4. The x terms cancel, leaving 2y = 6, so y = 3. Check: x = 7 and y = 3 satisfy both equations.

Which of the following gives all real solutions to sqrt(x + 7) = x - 5?

D. x = 9 only. Square both sides: x + 7 = x^2 - 10x + 25. Rearrange and factor: x^2 - 11x + 18 = 0, so (x - 2)(x - 9) = 0. Check x = 9: sqrt(16) = 4 and 9 - 5 = 4, so it works. Check x = 2: sqrt(9) = 3 but 2 - 5 = -3, so x = 2 is extraneous.

ACT Math reporting category

ACT Algebra Practice

Algebra is the ACT math reporting category about writing, rewriting, and solving expressions, equations, inequalities, and systems, including linear, quadratic, polynomial, radical, and exponential forms. According to ACT, it makes up 17–20% of scored math questions, as part of Preparing for Higher Math.

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17–20% of scored Math questions3 original questionsInstant answer checks

At a glance

Algebra on the ACT: the key numbers

Section and category facts from ACT.org, checked October 9, 2026. Time per question is ACT's section time divided by its question count.
Section	ACT Math: 45 questions in 50 minutes
Scored questions	41 scored, 4 field test
Reporting category	Algebra (part of Preparing for Higher Math)
Share of scored questions	17–20%, according to ACT
Average time per question	About 67 seconds
Counts toward the Composite	Yes
Practice on this page	3 original questions: Easy, Medium, Hard

What this tests

What does ACT Algebra test?

Linear equations and inequalities. Solve one-variable equations and inequalities, and write a linear equation or inequality that matches a described situation.
Systems of equations. Solve two linear equations together by substitution or elimination, and interpret what the solution means.
Quadratic equations. Solve by factoring, completing the square, or the quadratic formula, and connect the solutions to the factors.
Polynomial and radical expressions. Add, multiply, and factor polynomials, and solve equations with square roots while checking for extraneous solutions.
Exponential expressions. Rewrite expressions with exponents and solve simple equations in which the variable is in the exponent.

Practice questions

Practice ACT Algebra questions

Pick an answer to check it. Each question has one correct choice.

Question 1 of 3Easy

x + y = 10

and

x - y = 4

, what is the value of

y

Show answer and explanation

Correct answerA. $3$

How to solve it

Subtract the second equation from the first: $(x + y) - (x - y) = 10 - 4$ .
The $x$ terms cancel, leaving $2 y = 6$ , so $y = 3$ .
Check: $x = 7$ and $y = 3$ satisfy both equations.

Why the other choices miss

6

is the value of

2 y

; it skips the last step of dividing by 2.

7

is the value of

x

, not

y

14

2 x

, which comes from adding the two equations and then stopping.

Question 2 of 3Medium

What is the sum of the solutions to

2 x^{2} + 5 x - 12 = 0

Show answer and explanation

Correct answerC. $- \frac{5}{2}$

How to solve it

Factor: $2 x^{2} + 5 x - 12 = (2 x - 3) (x + 4)$ .
Set each factor equal to 0: $x = \frac{3}{2}$ or $x = - 4$ .
Add: $\frac{3}{2} + (- 4) = - \frac{5}{2}$ . This matches the shortcut $- \frac{b}{a} = - \frac{5}{2}$ .

Why the other choices miss

- \frac{11}{2}

solves

2 x - 3 = 0

x = - \frac{3}{2}

, a sign error.

- 5

uses

- b

but forgets to divide by

a = 2

\frac{5}{2}

drops the negative sign in

- \frac{b}{a}

Question 3 of 3Hard

Which of the following gives all real solutions to

x + 7 = x - 5

Show answer and explanation

Correct answerD. $x = 9$ only

How to solve it

Square both sides: $x + 7 = x^{2} - 10 x + 25$ .
Rearrange and factor: $x^{2} - 11 x + 18 = 0$ , so $(x - 2) (x - 9) = 0$ .
Check $x = 9$ : $16 = 4$ and $9 - 5 = 4$ , so it works.
Check $x = 2$ : $9 = 3$ but $2 - 5 = - 3$ , so $x = 2$ is extraneous.

Why the other choices miss

Choosing both 2 and 9 skips checking the solutions in the original equation.

- 2

and

- 9

come from factoring with the wrong signs. "No real solutions" comes from squaring

x - 5

x^{2} + 25

, which gives

x^{2} - x + 18 = 0

, an equation with no real roots.

Avoid these traps

What mistakes do students make on Algebra?

Skipping the extraneous check

Squaring both sides of a radical equation can create solutions that fail the original equation. Students who skip the check keep them.

Fix: Substitute every solution into the original equation. A square root can never equal a negative number.

Sign errors when factoring

Students factor $x^{2} - 11 x + 18$ as $(x + 2) (x + 9)$ because 2 and 9 multiply to 18, but those signs give the wrong middle term.

Fix: Expand your factors to check the middle term before you solve.

Answering for the wrong variable

In systems, students solve for $x$ and stop, even when the question asks for $y$ or for an expression such as $x + y$ .

Fix: Underline what the question asks for, and reread it before choosing an answer.

Study method

How should you practice ACT Algebra?

Start each problem by writing what it asks for, such as $y$ , the sum of the solutions, or every real solution.
Show every algebra step on paper. Many algebra misses come from a single dropped sign, not from a missing method.
Check answers by substituting them into the original equation, especially after squaring both sides.
Practice systems with both substitution and elimination so you can choose the faster one.
Do short daily Algebra sets in Dolphin, and review each missed question the same day.

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FAQ

Questions about ACT Algebra

What does the ACT Algebra category cover?

It covers expressions, equations, and inequalities in linear, quadratic, polynomial, radical, and exponential forms, along with systems of equations. The three questions on this page practice a linear system, the sum of the solutions to a quadratic, and a radical equation with an extraneous solution.

How is Algebra different from Functions on the ACT?

ACT reports them as separate categories, each at 17–20% of scored math questions. In general, Algebra focuses on rewriting and solving equations and inequalities, while Functions focuses on function notation, graphs, and how inputs relate to outputs. Many problems draw on both skills.

What is Preparing for Higher Math?

Preparing for Higher Math is the ACT reporting category that groups Number & Quantity, Algebra, Functions, Geometry, and Statistics & Probability. According to ACT, it makes up 80% of scored math questions, and Algebra alone accounts for 17–20%.

How should I study Algebra if I keep making careless errors?

Label every miss by type: sign error, distribution error, wrong variable, or no check. Then add one habit aimed at your most common type, such as expanding factors to confirm them or substituting answers back into the original equation.

Does Algebra count toward my ACT Composite score?

Yes, through your math score. The Composite is the average of your English, math, and reading scores, rounded. Science and writing are optional and do not affect the Composite.

Related practice

Sources

Where these facts come from

ACT: Understanding Your ACT Scores: reporting categories, category shares, Composite calculation, and scoring.
ACT: Test Enhancements and Changes: section length, question counts, and optional Science.
ACT: Official test preparation and free practice tests: released ACT questions in the real test format.

ACT facts checked October 9, 2026. Every practice question on this page is original Dolphin practice written to match one ACT reporting category. None is a released ACT item.

ACT® is a trademark registered by ACT, Inc., which is not affiliated with, and does not endorse, Dolphin.

ACT Algebra Practice

Algebra on the ACT: the key numbers

What does ACT Algebra test?

Practice ACT Algebra questions

How to solve it

How to solve it

How to solve it

What mistakes do students make on Algebra?

Skipping the extraneous check

Sign errors when factoring

Answering for the wrong variable

How should you practice ACT Algebra?

Questions about ACT Algebra

Keep practicing for the ACT

Where these facts come from