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# Algebra

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For what value of the constant a does the system of equations below have infinitely many solutions?

2x + 5y = -8

6x = 16 + a - 15y + 4x + 10y

Jul 12, 2022

#1
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Solve with substitution:

2x = -8 - 5y

$$x = -4 - \frac{5}{2}y$$

Substitute into the second equation:

$$6(-4-\frac{5}{2}y) = 16+a-15y+4(-4-\frac{5}{2}y) +10y$$

$$\rightarrow -24-15y=16+a-15y-16-10y+10y$$

Simplify:

-24 = a

So, for the system to have infinite solutions, a = -24.

Jul 12, 2022