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# System

-1
110
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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
+2448
0

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