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

4x + ay = -8

3x - y = b

 Jan 31, 2022
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Simplify the first equation to \(4x=-8-ay\).

Simplify the second equation to \(3x=b+y\).

Multiply this equation by \(4 \over 3\).

This equals \(4x= {4 \over 3} b + {4\over3}y\).

For \(4x=-8-ay \) and \(4x={4\over3}b+{4\over3}y\) to have infinite intersection points, they have to be the same. 

So... \(\color{brown}\boxed {a=-{3\over4}, b = -6}\)

 Jan 31, 2022

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