How do I solve by the elimination method

9x-y=75
x+y=15

9x-y=75

x+y=15

Add the two equations.

10x = 90

Can you take it from there?

To solve the given system of equations using the elimination method, follow these steps:

1. Align the equations vertically so that the variables and constant terms are in the same columns. Your system of equations should look like:
9x - y = 75
x + y = 15

2. Choose one variable (x or y) to eliminate. In this case, let's eliminate the variable y. To do this, you need to make the coefficient of y in both equations the same, but with opposite signs.

Multiply the second equation by -1 to change the sign of every term:
-1(x + y) = -1(15)
-x - y = -15

3. Add the two equations together. This will eliminate the variable y.
(9x - y) + (-x - y) = 75 + (-15)

Simplify the equation:
8x - 2y = 60

4. Now, solve the resulting equation for one variable. Let's solve for x. Rearrange the equation to isolate x:
8x - 2y = 60
8x = 2y + 60
Divide both sides by 8:
x = (2y + 60)/8
Simplify further if necessary.

5. Substitute the value of x obtained into one of the original equations to solve for the other variable. Let's substitute x in the first equation:
9x - y = 75
9((2y + 60)/8) - y = 75
Simplify the equation and solve for y.

6. Once you have the value of one variable, substitute it back into one of the original equations to find the value of the other variable.

By following these steps, you will be able to solve the system of equations using the elimination method.