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SAT Math

Systems of Linear Equations

Systems of Linear Equations is a skill in the Algebra domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.

11 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.

Round length
Difficulty (none selected means all)

Sample questions

Open a question to see the answer choices and the correct answer.

A community theater sold adult and child tickets to a play. The equations 3a + 2c = 52 and 2a + 5c = 64 represent the situation, where a is the price, in dollars, of an adult ticket and c is the price, in dollars, of a child ticket. What is the price of an adult ticket?
  1. A. $32
  2. B. $12 ✓
  3. C. $9.67
  4. D. $8

Correct answer: B. Solving the system (for example, by elimination) gives a = 12 and c = 8, so an adult ticket costs $12.

How many solutions does the system of equations below have? 6x − 9y = 18 4x − 6y = 15
  1. A. Infinitely many solutions
  2. B. Exactly one solution
  3. C. No solution ✓
  4. D. Exactly two solutions

Correct answer: C. Dividing the first equation by 3 gives 2x − 3y = 6, and dividing the second by 2 gives 2x − 3y = 7.5; since the same left side cannot equal two different values, the lines are parallel and distinct, so there is no solution.

If 4x + 3y = 26 and x + 3y = 11, what is the value of x?
  1. A. 15
  2. B. 2
  3. C. −5
  4. D. 5 ✓

Correct answer: D. Subtracting the second equation from the first eliminates y: (4x + 3y) − (x + 3y) = 26 − 11, giving 3x = 15, so x = 5.

A farm stand sells apples for $2 each and peaches for $3 each. On one day, the stand sold 50 total pieces of fruit for a combined total of $130. How many peaches were sold?
  1. A. 30 ✓
  2. B. 20
  3. C. 26
  4. D. 43

Correct answer: A. Correct — from a + p = 50 and 2a + 3p = 130, substituting a = 50 − p gives 2(50 − p) + 3p = 130, so 100 + p = 130 and p = 30.

For what value of k does the system 2x + 3y = 7 and 4x + ky = 9 have no solution?
  1. A. 3.5
  2. B. 6 ✓
  3. C. 9
  4. D. 1.5

Correct answer: B. Correct — for a system of two linear equations to have no solution, the lines must be parallel but not identical; matching the ratio of coefficients gives 4/2 = k/3, so k = 6 (and since 9 ≠ 2 × 7, the lines are indeed parallel and distinct).