The rules that solve most questions
- Elimination: multiply one or both equations so a variable has opposite coefficients, then add (or matching coefficients, then subtract).
- Substitution: when one equation already says y = … or x = …, plug it into the other.
- Read the question: it may ask for x + y or 2x − y, which you can sometimes get by adding or subtracting the equations directly.
- If two equations have the same slope and different intercepts, there is no solution; if they're the same line, there are infinitely many.
Traps the wrong answers are built on
- Solving for x and stopping when the question asks for x + y.
- Multiplying only one side of an equation.
- Sign errors when subtracting equations.
Worked example
2x + 3y = 25
2x + 2y = 20
If (x, y) is the solution to the system of equations above, what is the value of x?
- A. 5
- B. 10
- C. 6
- D. −5
Answer: A. Eliminate one variable. Multiply the first equation by 2 and the second by 3, then subtract: −2x = −10. So x = 5. Substitute into the first equation: 2(5) + 3y = 25, so y = 5. The question asks for x: 5.
Practice set
Answer each question to see whether you're right and why. When you finish, draw a new set: the numbers change every time.
0 of 10 answered · 0 correct · set 1
- Question 1Medium
2x + 3y = 25
2x + 2y = 20
If (x, y) is the solution to the system of equations above, what is the value of x?
Show answer and explanation
Answer: A
Eliminate one variable. Multiply the first equation by 2 and the second by 3, then subtract: −2x = −10.
So x = 5. Substitute into the first equation: 2(5) + 3y = 25, so y = 5.
The question asks for x: 5.
- Question 2Medium
2x + 2y = 30
2x − 4y = −18
If (x, y) is the solution to the system of equations above, what is the value of x?
Show answer and explanation
Answer: D
Eliminate one variable. Multiply the first equation by −4 and the second by 2, then subtract: −12x = −84.
So x = 7. Substitute into the first equation: 2(7) + 2y = 30, so y = 8.
The question asks for x: 7.
- Question 3Medium
3x + y = 23
5x + 3y = 33
If (x, y) is the solution to the system of equations above, what is the value of x + y?
Show answer and explanation
Answer: D
Eliminate one variable. Multiply the first equation by 3 and the second by 1, then subtract: 4x = 36.
So x = 9. Substitute into the first equation: 3(9) + y = 23, so y = −4.
The question asks for x + y = 9 + (−4) = 5.
- Question 4Medium
5x + 5y = 0
5x + 3y = −10
If (x, y) is the solution to the system of equations above, what is the value of x + y?
Show answer and explanation
Answer: B
Eliminate one variable. Multiply the first equation by 3 and the second by 5, then subtract: −10x = 50.
So x = −5. Substitute into the first equation: 5(−5) + 5y = 0, so y = 5.
The question asks for x + y = −5 + 5 = 0.
- Question 5Medium
4x − 2y = 20
3x − 4y = 5
If (x, y) is the solution to the system of equations above, what is the value of x + y?
Show answer and explanation
Answer: C
Eliminate one variable. Multiply the first equation by −4 and the second by −2, then subtract: −10x = −70.
So x = 7. Substitute into the first equation: 4(7) − 2y = 20, so y = 4.
The question asks for x + y = 7 + 4 = 11.
- Question 6Medium
5x + 4y = −6
x + 4y = 2
If (x, y) is the solution to the system of equations above, what is the value of x?
Show answer and explanation
Answer: A
Eliminate one variable. Multiply the first equation by 4 and the second by 4, then subtract: 16x = −32.
So x = −2. Substitute into the first equation: 5(−2) + 4y = −6, so y = 1.
The question asks for x: −2.
- Question 7Medium
5x − 2y = 22
4x − 4y = 20
If (x, y) is the solution to the system of equations above, what is the value of x + y?
Show answer and explanation
Answer: A
Eliminate one variable. Multiply the first equation by −4 and the second by −2, then subtract: −12x = −48.
So x = 4. Substitute into the first equation: 5(4) − 2y = 22, so y = −1.
The question asks for x + y = 4 + (−1) = 3.
- Question 8Medium
2x − 2y = 8
5x + 2y = 13
If (x, y) is the solution to the system of equations above, what is the value of x?
Show answer and explanation
Answer: B
Eliminate one variable. Multiply the first equation by 2 and the second by −2, then subtract: 14x = 42.
So x = 3. Substitute into the first equation: 2(3) − 2y = 8, so y = −1.
The question asks for x: 3.
- Question 9Medium
5x − 4y = −2
5x − 3y = 6
If (x, y) is the solution to the system of equations above, what is the value of x + y?
Show answer and explanation
Answer: A
Eliminate one variable. Multiply the first equation by −3 and the second by −4, then subtract: 5x = 30.
So x = 6. Substitute into the first equation: 5(6) − 4y = −2, so y = 8.
The question asks for x + y = 6 + 8 = 14.
- Question 10Medium
4x + 5y = 19
3x − 4y = −9
If (x, y) is the solution to the system of equations above, what is the value of x?
Show answer and explanation
Answer: D
Eliminate one variable. Multiply the first equation by −4 and the second by 5, then subtract: −31x = −31.
So x = 1. Substitute into the first equation: 4(1) + 5y = 19, so y = 3.
The question asks for x: 1.
More Algebra practice
Questions people ask
Is this systems of linear equations practice like the real SAT?
The questions follow the format of the digital SAT's Algebra domain: four answer choices built from common mistakes. They are written for this site; they are not official College Board questions.
How many practice questions are there?
As many as you want. Each math question is generated from a template with new numbers, and its answer is checked by code. Use "New set" for another ten.
Where is the domain on the test?
Algebra is one of the four content domains of the SAT Math section, alongside Advanced Math, Problem-Solving and Data Analysis, Geometry and Trigonometry.