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# Hard Problem

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For what value of the constant $a$ does the system of equations below have infinitely many solutions?\begin{align*} 2x + 5y &= -8,\\ 6x &= 16 + a - 15y \end{align*}

Jul 9, 2022

#1
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In order for a system to have infinitely many solutions, the equations must represent the same coefficients and constants.

We have the equations:

2x + 5y = - 8

6x + 15y = 16 + a

Multiplying the first equation by 3 gives us:

6x + 15y = -24

6x + 15y = 16 + a

In order for this system to have infintely many solutions, 16 + a = -24

This gives us -40 for a.

Jul 9, 2022
#2
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How do you vote up?

Jul 9, 2022
#3
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Upvoting only works when you are currently logged in, I believe.

But if logged in, you may always hover over the heart next to the post and select either thumbs up or thumbs down. :)

Jul 9, 2022