SAT Math · Algebra
Systems of two linear equations in two variables practice questions
Each free question on this page comes with its answer and a full explanation, and each one is marked easy, medium or hard.
- Question 4 · mediumThe system of equations 2x + 5y = 10 and 6x + ky = 30 has infinitely many solutions. What is the value of k?
- Question 5 · easyIf 3x + 2y = 22 and x - 2y = 2, what is the value of x?
- Question 7 · mediumA theater sold 150 tickets for a play, some at $12 for adults and the rest at $7 for children. Total ticket sales were $1,400.…
- Question 28 · mediumFor what value of k does the system 2x + 3y = 9 and 4x + ky = 20 have no solution?
- Question 58 · mediumThe lines y = 3x - 2 and y = -x + 14 intersect at a point. Is the y-coordinate of that point greater than or less than 7?
- Question 59 · hardThe system x + y = 10 and x - y = k has a solution in Quadrant I (where both x > 0 and y > 0) for a range of values of k. What…
- Question 73 · mediumThe equations x + y = 5 and 2x + 2y = 10 describe the same line. If a third equation, x - y = 1, is added to form a system of…
- Question 92 · easyIf 3x + 2y = 16 and x - 2y = -4, what is the value of x?
- Question 112 · easyThe system 2x + ky = 14 and x - y = 1 has solution (5, 4). What is the value of k?
- Question 113 · mediumIf 1/3x + 1/2y = 7 and x + y = 15, what is the value of y?
- Question 149 · mediumAn investor puts a total of $8,000 into two accounts, one earning 4% annual interest and the other earning 7% annual interest.…
- Question 150 · hardThe line kx + my = 26 passes through the point (3, 4) and the equation kx + 4my = 22 (using the same k and m) is satisfied by…
- Question 170 · mediumThe system ax + 3y = 12 and 4x + by = 24 has infinitely many solutions. If a = 2, what is the value of b?
- Question 188 · easyThe system 3x + ky = 21 and x + y = 7 has solution (4, 3). What is the value of k?
- Question 209 · easyIf 2x + 3y = 19 and 4x - 3y = 5, what is the value of 6x?
- Question 225 · mediumA concert sold 300 tickets, some at $15 for general admission and the rest at $20 for VIP. Total ticket sales were $5,000. How…
- Question 268 · easyThe system 5x + ky = 29 and x - y = 1 has solution (3, 2). What is the value of k?
- Question 286 · easyThe system 4x + ky = 48 and 2x - y = 8 has solution (6, 4). What is the value of k?
- Question 306 · easyThe system 3x + ky = 33 and x - y = 4 has solution (7, 3). What is the value of k?
- Question 321 · hardThe system kx + 4y = 20 and 3x + 2y = 10 has infinitely many solutions. What is the value of k?
- Question 324 · hardThe system 4x + ky = 8 and 2x + 3y = m has no solution when k = 6 and m = 5. For which value of m would the system have…