Short Answer 
To solve a system of equations, first set the equations equal to each other and solve for x. Then substitute the value of x back into one of the original equations to find y, resulting in the solution (x, y) = (-2, -6).
Step 1: Set the Equations Equal to Each Other
Begin by expressing both equations in a format that allows for direct comparison. For example, if you have the equations x – 4 and 4x + 2, you set them equal to each other to form:
- x – 4 = 4x + 2
Step 2: Solve for x
Next, manipulate the equation to isolate x. This generally involves moving all terms involving x to one side and constant terms to the other. You will end up with:
- -3x = 6
- x = -2
Step 3: Substitute x Back to Find y
Once you have the value of x, plug it back into one of the original equations to determine y. For example, using the equation y = x – 4, substitute x = -2:
- y = -2 – 4
- y = -6
Thus, the solution to the system is x = -2 and y = -6, with the point of intersection being (-2, -6).