SAT linear equations practice

Turn an equation into two graphs. Find the intersection, then check which coordinate the question asks for.

The idea to remember

An intersection satisfies both equations. Its x-coordinate and y-coordinate answer different questions.

A worked example

For y = 2x + 1 and y = -x + 7, equate the expressions: 2x + 1 = -x + 7. Then 3x = 6, so x = 2 and y = 5.

A common trap

Selecting 5 when the question asks for x confuses the coordinates of the same correct intersection.

For a longer walkthrough, read How to solve SAT linear equations with a graph.

By Graph Math Practice editorial team · Reviewed 2026-09-05

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All 8 questions, with explanations

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1. The lines y = 2x + 1 and y = -x + 7 intersect. What is the x-coordinate of their intersection?
1. 2
2. 5
3. 3
4. -2
Show answer and explanation
Answer: A. 2
Set 2x + 1 = -x + 7. This gives 3x = 6, so x = 2. Substitution gives y = 5. On a graph, read the x-coordinate of the intersection, not its height.
2. What value of x satisfies 2(x + 1) = 10 - 2x?
1. 4
2. -2
3. 6
4. 2
Show answer and explanation
Answer: D. 2
Expand the left side: 2x + 2. Move 2x to the left and subtract 2 from both sides. Then 4x = 8, so x = 2. Alternatively graph y = 2(x + 1) and y = 10 - 2x and read the intersection x-coordinate.
3. The lines y = 3x + 2 and y = -x + 14 intersect. What is the x-coordinate of their intersection?
1. 4
2. -3
3. 3
4. 11
Show answer and explanation
Answer: C. 3
Set 3x + 2 = -x + 14. This gives 4x = 12, so x = 3. Substitution gives y = 11. On a graph, read the x-coordinate of the intersection, not its height.
4. What value of x satisfies 3(x + 2) = 21 - 2x?
1. 15
2. 3
3. 5
4. -3
Show answer and explanation
Answer: B. 3
Expand the left side: 3x + 6. Move 2x to the left and subtract 6 from both sides. Then 5x = 15, so x = 3. Alternatively graph y = 3(x + 2) and y = 21 - 2x and read the intersection x-coordinate.
5. The lines y = 4x + 3 and y = -x + 23 intersect. What is the x-coordinate of their intersection?
1. 4
2. 19
3. 5
4. -4
Show answer and explanation
Answer: A. 4
Set 4x + 3 = -x + 23. This gives 5x = 20, so x = 4. Substitution gives y = 19. On a graph, read the x-coordinate of the intersection, not its height.
6. What value of x satisfies 4(x + 3) = 36 - 2x?
1. 6
2. -4
3. 28
4. 4
Show answer and explanation
Answer: D. 4
Expand the left side: 4x + 12. Move 2x to the left and subtract 12 from both sides. Then 6x = 24, so x = 4. Alternatively graph y = 4(x + 3) and y = 36 - 2x and read the intersection x-coordinate.
7. The lines y = 5x + 4 and y = -x + 34 intersect. What is the x-coordinate of their intersection?
1. 6
2. -5
3. 5
4. 29
Show answer and explanation
Answer: C. 5
Set 5x + 4 = -x + 34. This gives 6x = 30, so x = 5. Substitution gives y = 29. On a graph, read the x-coordinate of the intersection, not its height.
8. What value of x satisfies 5(x + 4) = 55 - 2x?
1. 45
2. 5
3. 7
4. -5
Show answer and explanation
Answer: B. 5
Expand the left side: 5x + 20. Move 2x to the left and subtract 20 from both sides. Then 7x = 35, so x = 5. Alternatively graph y = 5(x + 4) and y = 55 - 2x and read the intersection x-coordinate.

Scope reference: College Board’s section overview. Questions are independently authored and are not official exam material.

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