Answer:
The solution to this system of equations is x = 8, and y = -9
Step-by-step explanation:
Firstly we need to use the first equation to represent "x" in terms of "y", so we do the following...
[tex]5x + 3y = 13\\5x = 13 - 3y\\x = \frac{13}{5} - \frac{3}{5}y[/tex]
Now we take the second equation and replace "x" with an equal value in terms of "y" which we know from the previous equation, and just solve for "y".
[tex]7x + 8y = -16\\7(\frac{13}{5} -\frac{3}{5} y) + 8y = -16\\\\18\frac{1}{5} - 4\frac{1}{5} y + 8y = -16\\\\3\frac{4}{5}y = -34\frac{1}{5} \\\\y = -34\frac{1}{5} / 3\frac{4}{5} \\y = -9[/tex]
After we found the value of "y" we can find the value of "x" by using any of the two equations, we just have put "-9" instead of "y". For example...
[tex]5x + 3y = 13\\5x + 3(-9) = 13\\5x - 27 = 13\\5x = 13 + 27\\5x = 40\\x = 40 / 5\\x = 8[/tex]
Now we know that the solution to this system of equations is x = 8, and y = -9
