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# system equations

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For what ordered pair (a,b) are there infinite solutions (x,y) to the system

4x + ay = -8

2x - 3y = b

May 2, 2022

#1
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For the system to have infinite solutions, the equations have to be multiples of each other.

The first equation needs to be double the second, because of the ratio of the coefficients of x.

Multiplying the second equation by 2 gives us \(4x - 6y = 2b\)

We have that \(a = -6\), and \(2b=-8\), meaning \(b =-4\)

Thus, the desired pair is \(\color{brown}\boxed{( -6,-4)}\)

May 2, 2022