I'm doing solving systems by substitution and need finding the intersection between y=2x+2 and 7x-5y=-9. can anyone give me the answer and the work behind it?

The substitution method of solving a system of 2 equations in 2 variables.
1) Solve one equation for one variable.
2) Substitute what that variable is equal to in the other equation.
3) Solve the equation for the only variable in it.
4) Substitute the value you obtained into one of the original equations and solve for the other variable.

The above is the explanation of the method.
Now we will solve your system of equations going through each step.

1) Solve one equation for one variable.
Look at your equations. The second equation is already solved for y, so you can just use the fact that y is the same as 2x + 2.

2) Substitute what that variable is equal to in the other equation.
Now we substitute 2x + 2 in for y of the second equation.
Here is the original second equation:

7x - 5y = -9

We substitute y with 2x + 2. We must use parentheses.
7x - 5(2x + 2) = -9

3) Solve the equation for the only variable in it.
We distribute the -5, collect like terms, and solve for x.

7x - 10x - 10 = -9

-3x - 10 = -9

-3x = 1

x = -1/3

4) Substitute the value you obtained into one of the original equations and solve for the other variable.

y = 2x + 2

y = 2(-1/3) + 2

y = -2/3 + 6/3

y = 4/3

The solution is: x = -1/3 and y = 4/3