how does the substitution method work?

Question

anonymous · Answer

The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.
For example:
2x – 3y = –2
4x +   y = 24

I'll solve the second equation for "y"
4x + y = 24
y = –4x + 24

Now I'll plug this in ("substitute it") for "y" in the first equation, and solve for x:

2x – 3(–4x + 24) = –2
2x + 12x – 72 = –2
14x = 70
x = 5

Now you can substitute x into the equation 4x +   y = 24
y = –4(5) + 24 = –20 + 24 = 4

The solution set is (x, y) = (5, 4).