Substitution method:
Solve with the solution: with checking
y=8x-12
-4x-4y=-8
To solve the system of equations using the substitution method, we will solve the first equation for y and substitute it into the second equation.
Given:
1) y = 8x - 12
2) -4x - 4y = -8
Solve the first equation (1) for y:
y = 8x - 12
Substitute y in the second equation (2) with 8x - 12:
-4x - 4(8x - 12) = -8
Expand and simplify the equation:
-4x -32x + 48 = -8
-36x + 48 = -8
-36x = -8 - 48
-36x = -56
Divide both sides by -36 to isolate x:
x = -56 / -36
x = 14/9
Now substitute the value of x back into equation (1) to solve for y:
y = 8(14/9) - 12
y = 112/9 - 108/9
y = 4/9
Therefore, the solution to the system of equations is x = 14/9 and y = 4/9.