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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.

Practice systems of equations in DolphinPractice questions
12-18 min practice time3 questions on pageHeart of Algebra
Practice time12-18 min
Question bank3 questions
Best forHeart of Algebra

What this tests

What to know for this SAT skill

Dolphin question bank

Practice your skill

Question 1 of 3Easy
If x + y = 10 and x - y = 2, what is the value of x?
  1. 4
  2. 5
  3. 6
  4. 8
Show answer and solution
Correct answerC. 6

Solution walkthrough

  1. Add the equations to eliminate y: 2x = 12.
  2. Divide by 2, so x = 6.
Question 2 of 3Medium
If 2x + 3y = 18 and x = 3, what is the value of y?
  1. 3
  2. 4
  3. 5
  4. 6
Show answer and solution
Correct answerB. 4

Solution walkthrough

  1. Substitute x = 3 into 2x + 3y = 18.
  2. That gives 6 + 3y = 18, so 3y = 12 and y = 4.
Question 3 of 3Hard
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?
  1. 15
  2. 20
  3. 25
  4. 30
Show answer and solution
Correct answerB. 20

Solution walkthrough

  1. Let a be adult tickets and s be student tickets.
  2. Then a + s = 40 and 12a + 8s = 400.
  3. 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

  1. Decide whether substitution or elimination is faster before doing arithmetic.
  2. Label variables clearly when the system comes from a word problem.
  3. Solve for the requested value, not just the first variable that appears.
  4. Plug the answer back into both equations to catch sign mistakes.
Practice systems of equations in Dolphin

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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.