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.
