Solve the system by using the substitution method.
y= 3/4x - 4
-x + 2y= -6
To solve a system of equations using the substitution method, we need to solve one equation for one variable and then substitute it into the other equation. Let's solve the first equation for y:
y = (3/4)x - 4
Now, substitute this expression for y into the second equation:
-x + 2y = -6
-x + 2((3/4)x - 4) = -6
Simplify the equation by distributing the 2:
-x + (3/2)x - 8 = -6
Combine like terms:
(3/2)x - x - 8 = -6
Multiply every term by 2 to get rid of the fraction:
3x - 2x - 16 = -12
Combine like terms again:
x - 16 = -12
Add 16 to both sides of the equation:
x = 4
Now that we have the value of x, we can substitute it back into the first equation to find the value of y:
y = (3/4)(4) - 4
y = 3 - 4
y = -1
Therefore, the solution to the system of equations is x = 4 and y = -1.