Solve systems of two linear equations using elimination or substitution, and reason about when systems have one, none, or infinite solutions.
92 original systems of linear equations questions in the SAT Ranker bank, with instant scoring and an Elo-based rank once you sign up. Below are a few free samples with full explanations.
A system has infinitely many solutions: 4x + 6y = 12 and 2x + ky = 6. What is the value of k?
Divide the first equation by 2: 2x + 3y = 6. For infinitely many solutions, this must match the second equation exactly, so k = 3.
If 2x + y = 10 and x − y = 2, what is the value of x?
Add the two equations: (2x + y) + (x − y) = 12, so 3x = 12, x = 4.
If 3x − 2y = 4 and x + 2y = 12, what is the value of x?
Adding the two equations eliminates y: (3x − 2y) + (x + 2y) = 4 + 12, so 4x = 16, giving x = 4.
If 3x + 2y = 11 and 1x + 4y = -23, what is the value of x?
Solving the system gives x = 9 and y = -8, so x = 9.
If 5x + 6y = -76 and 6x + 2y = -60, what is the value of y?
Solving the system gives x = -8 and y = -6, so y = -6.