Drill 3 · Math · Systems of Equations
SAT Math: Systems of Equations (Drill 3) 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 cover substitution and elimination strategies, analyzing systems to determine the number of solutions, and interpreting what the intersection of two lines or curves represents in applied contexts.
Question 1. 2x − y = 7 and x + y = 5. What is the value of x?
Explanation: Add the equations: 3x = 12, so x = 4. Substitute: 4 + y = 5, y = 1.
Question 2. A store sells notebooks for $4 and pens for $2. A customer buys 12 items totaling $36. How many notebooks did they buy?
Explanation: n + p = 12 and 4n + 2p = 36. From the first: p = 12 − n. Substitute: 4n + 2(12 − n) = 36 → 2n + 24 = 36 → n = 6.
Question 3. For what value of a does the system 2x + 3y = 12 and 4x + ay = 15 have no solution?
Explanation: No solution means parallel lines. Multiply equation 1 by 2: 4x + 6y = 24. For the same left side, a = 6. Then 4x + 6y = 24 vs. 4x + 6y = 15, parallel.
Question 4. y = 2x + 1 and y = 2x − 5. How many solutions does this system have?
Explanation: Both lines have slope 2 but different y-intercepts (1 and −5). Parallel lines never intersect, so zero solutions.
Question 5. 5x + 2y = 20 and 3x − 2y = 4. What is the value of y?
Explanation: Add equations: 8x = 24, x = 3. Substitute into 5(3) + 2y = 20: 15 + 2y = 20, 2y = 5, y = 2.5.