Now that you know x, finding y is a breeze. Just plug your x back into the
second equation. Then solve for y.
The trick to which method to use depends on what kind of system you’re
dealing with. If each x and y in the system has a coefficient (that’s the fancy
name for a number that’s multiplying a variable), you’ll want to stick with
elimination. If one of the variables is all alone, go with substitution.
Whether you use elimination or substitution, you still might not be able to solve
x and y for both equations. For example, in the equations:
No matter how you manipulate those equations, you will never find an x and
y that satisfy both of them. What’s going on here? Well, the answer might be
clear if we convert both to slope-intercept form:
The first equation: 4y = 3x + 28The second equation: