Short Answer 
To solve the system of equations y = x – 4 and y = 4x + 2, first set them equal to each other, resulting in x – 4 = 4x + 2. After solving for x, you find x = -1.5, and substituting this value back into one of the original equations gives y = -5.5, leading to the intersection point (-1.5, -5.5).
Step 1: Set the Equations Equal
Start by writing down the two equations that you want to solve: y = x – 4 and y = 4x + 2. Since both equations equal y, you can set them equal to each other to find their intersection point. This gives you the equation:
- x – 4 = 4x + 2
Step 2: Solve for x
Next, simplify the equation you created in Step 1 to solve for x. Rearranging the equation, you get:
- x – 4 – 4x = 2
- -3x – 4 = 2
- -3x = 6
- x = -1.5
At this point, you have found x.
Step 3: Substitute to Find y
To find the corresponding value of y, substitute x = -1.5 back into one of the original equations. Using y = x – 4, replace x with -1.5, which results in:
- y = -1.5 – 4
- y = -5.5
Therefore, the solution to the system of equations is the point (-1.5, -5.5).