Final answer:
The solution to the system of equations y = x - 4 and y = 4x + 2 is obtained by setting the right-hand sides equal to each other, solving for x to get x = -2, and then substituting x into one of the equations to find y = -6.
Step-by-step explanation:
To find the solution to the system of equations y = x - 4 and y = 4x + 2, we can use the method of substitution or set the equations equal to each other since they both equal y. By setting the right sides of the equations equal to each other, we get:
x - 4 = 4x + 2
To solve for x, we gather all x terms on one side and the constant terms on the other:
-4 - 2 = 4x - x
-6 = 3x
Therefore, x = -2.
Now, substitute -2 for x in one of the original equations to solve for y:
y = (-2) - 4
y = -6.
So the solution to the system of equations is x = -2 and y = -6.