Drill 1 · Math · Systems of Equations
SAT Math: Systems of Equations (Drill 1) is a Math practice drill covering Systems of Equations. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.
SAT systems of equations questions involve solving two or more equations with two or more unknowns. You may use substitution or elimination, or recognize special cases where a system has no solution or infinitely many solutions. This drill includes both pure and applied problems.
Question 1. y = 2x + 1 and 3x + y = 16. What is the value of x in the solution to the system?
Explanation: Substitute y = 2x + 1 into 3x + y = 16: 3x + 2x + 1 = 16. So 5x = 15, x = 3.
Question 2. A movie theater sold 350 tickets. Adult tickets cost $12 each and child tickets cost $7 each. Total revenue was $3,400. How many adult tickets were sold?
Explanation: Let a = adult, c = child. a + c = 350 and 12a + 7c = 3,400. Substitute c = 350 − a: 12a + 7(350 − a) = 3,400. So 5a = 950, a = 190.
Question 3. 4x + 6y = 18 and 2x + 3y = 12. How many solutions does this system have?
Explanation: Divide the first equation by 2: 2x + 3y = 9. The second is 2x + 3y = 12. Same left side, different right sides (9 ≠ 12), parallel lines, zero solutions.
Question 4. 5x − 2y = 2 and 3x + 2y = 14. What is the value of y?
Explanation: Add equations: 8x = 16, x = 2. Substitute: 3(2) + 2y = 14, 2y = 8, y = 4.
Question 5. 6x − 9y = 12 and 2x − 3y = 4. How many solutions does this system have?
Explanation: Divide the first equation by 3: 2x − 3y = 4. Identical to the second equation, infinitely many solutions.