Example 1 Easy
If x + y = 10 and x - y = 2, what is the value of x?
- 4
- 5
- 6
- 8
Show answer and explanation
Answer: 6
Add the equations to eliminate y: 2x = 12. Divide by 2, so x = 6.
SAT Math skill page
SAT Systems of Equations Practice
Build the SAT Math skill behind solving two equations together and translating paired constraints into a clean system.
12-18 min practice time 3 examples on page Heart of Algebra
What this tests
What to know for this SAT skill
- Solve a system by substitution or elimination
- Translate two conditions into two equations
- Interpret the solution as a point or real-world value
- Check whether the question asks for x, y, or a combined expression
Practice examples
Try a few SAT-style questions
Example 2 Medium
If 2x + 3y = 18 and x = 3, what is the value of y?
- 3
- 4
- 5
- 6
Show answer and explanation
Answer: 4
Substitute x = 3 into 2x + 3y = 18. That gives 6 + 3y = 18, so 3y = 12 and y = 4.
Example 3 Hard
A theater sold 40 tickets. Adult tickets cost $12 and student tickets cost $8. If total revenue was $400, how many adult tickets were sold?
- 15
- 20
- 25
- 30
Show answer and explanation
Answer: 20
Let a be adult tickets and s be student tickets. Then a + s = 40 and 12a + 8s = 400. Subtract 8(a + s) = 320 from the revenue equation to get 4a = 80, so a = 20.
Avoid these traps
Common mistakes on this skill
Using only one condition
A systems question usually needs both equations. One equation alone leaves too many possible values.
Stopping at the wrong variable
The SAT may ask for y, x + y, or a real-world count rather than the first variable you solve.
Losing signs during elimination
When subtracting equations, rewrite the full line so negative terms do not flip accidentally.
Study plan
How to practice this skill in Dolphin
- Decide whether substitution or elimination is faster before doing arithmetic.
- Label variables clearly when the system comes from a word problem.
- Solve for the requested value, not just the first variable that appears.
- Plug the answer back into both equations to catch sign mistakes.
Related practice
Build the surrounding skills
FAQ
Questions about SAT Systems of Equations Practice
How often do systems of equations appear on SAT Math?
They appear regularly because they connect algebra, graphs, and word problems. The setup is often more important than the computation.
Should I use substitution or elimination on the SAT?
Use substitution when one variable is already isolated. Use elimination when coefficients line up or can be made to line up quickly.
What makes systems questions hard?
The hardest versions hide the two equations inside a word problem or ask for an expression instead of a single variable.