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Answer:

a = -40

Step-by-step explanation:

In order for a system of equations to have infinitely many solutions, the equations must have the same line when graphed. Knowing this, it also means that the equations equal the same thing - they're just written differently. Also, remember that a constant term is just a number with no variables.

First, I would organize the second equation into standard format just like the first one (moving the x and y terms to the left side):

[tex]6x = 16 + a -15y\\6x + 15y = 16 + a[/tex]

Then, by comparing the x and y terms in both equations, we can see that the second equation is just the first equation multiplied by 3. (Notice how 2x times 3 is 6x, and 5y times 3 is 15y.) So, we would need our constant on the left hand side to do the same, to equal -8 times 3, or -24.

Thus, we would need to find what added to 16 equals -24, and we can do this with a simple algebra equation:

[tex]a + 16 = -24\\a = -40[/tex]

Therefore, a would need to equal -40 in order for the system to have infinitely many solutions.

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