SAT Math · Systems of two linear equations in two variables · medium
For what value of k does the system 2x + 3y = 9 and 4x + ky = 20 have no solution?
For what value of does the system and have no solution?
Answer and explanation
Answer: A: 6
Multiply the first equation by 2 to compare it to the second: . A system has no solution when the lines are parallel, meaning the left sides have identical coefficients but the right sides differ. The second equation has , so must be 6, and the constants 18 and 20 differ, so the lines never meet. That gives choice A. Choice B (9) copies the constant from the first equation. Choice C (3) is the -coefficient of the original equation, which would make the lines intersect. Choice D (10) is the half of 20 and has no meaning in the system.
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