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# System

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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

#1
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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