We are asked to solve a system of equations using the substitution method:
y = 2 x + 1
5 y - 6 x = 13
So we use the first equation as our substitution for "y", since we know that y is equal to "2 x + 1"
We use this expression in the second equation replacing "y":
5 (2x + 1) - 6 x = 13
and now we solve for the only unknown "x" that was left in the equation. We use distributive property to get rid of the parenthesis:
10 x + 5 - 6 x = 13
we combine the terms in x and subtract 5 from both sides:
4 x = 13 - 5
4 x = 8
x = 8/4
x = 2
Now we use this result in the first equation (our substitution equation):
y = 2 (2) + 1 = 5
therefore, x = 2 and y = 5 are the solutions to the system, also written in coordiate pair form as: (2, 5).