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

4x+ay=-8-3x+y,
2x+y=b+2x+5y

 May 20, 2022
 #1
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I dont think such values exist. 

 

We can simplify the equations to:

 

\(4y+b = 0 \)

\(7x+ay=y-8\)

 

For both equations to have infinite solutions, the 2 equations must be multiples of each other. 

 

However, notice that the first equation has the slope \(-7 \over a\), and the second term has a slope of 0. 

 

Because the 2 slopes are different, there is no ordered pair (a,b) that satisfies the requirements. 

 May 20, 2022

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