# ACT , Algebra 1 – system of equations

MathPro Q&A Forum (ACT)

Q: For what value of A will the following system of equations have infinitely many solutions?

3x – 2y = 4

Ax + 4y = -8

Explanation: In order for the system to have infinitely many solutions, the two equations must describe the same line.  (Recall that the solution(s) of a system are the points where the graphs of the two lines meet.  For the two lines to meet in infinitely many points, they must be the same line.)

To make the second equation the same as the first, multiply both sides of the first equation by -2:

-2(3x – 2y) = -2(4)

-6x + 4y = -8

So, A = -6.

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