Since y = x - 2, replace the y in 8x + 13y = 2 with x - 2:
8x + 13(x - 2) = 2
Simplify the equation by multiplying 13 by (x - 2):
8x + 13x - 26 = 2
Add 26 on each side:
8x + 13x = 28
Add like terms:
21x = 28
Divide by 21 on each side:
x = 28/21
Simplify the fraction:
x = 4/3
Now that we have solved for x we can now use it to plug into one of the equations to solve for y. Plug in 4/3 for x in y = x - 2:
y = (4/3) - 2
Subtract:
y = -2/3
Let's check the work to make sure it is right:
8(4/3) + 13(-2/3) = 2
32/3 + -26/3 = 2
6/3 = 2
2 = 2
As you can see the system of equations has been solved correctly.
