1. Systems of Equations

2. Substitution
Substitution is a good method to use if one variable in one of the equations is already isolated or has a coefficient of one.

3. Substitution Step 1. Solve for one of the variables.
(look for the easiest)
Step 2. Plug the expression for the solved
variable into the other equation and
solve for the other variable.
Step 3. Plug into one of the equations to find the
other variable.
Step 4. Check your answer.

4. Substitution Solve the system using substitution. y = 4x x + 3y = –39
Since y is already isolated in the first equation,
substitute the value of y for y in the second equation.
The result is one equation with one variable.

5. Substitution After solving for x, solve for y by substituting
the value for x in any equation that contains 2 variables.
y = 4x y = 4(–3)
y = –12
Write the solution as an ordered pair. (–3, –12)

6. Substitution P P The solution is (– 3, –12).
Check the solution in BOTH equations.
y = 4x
x + 3y = –39
–12 = 4(–3)
–12 = –12
–3 + 3(– 12) = –39
–3 – 36 = –39
–39 = –39
The solution is (– 3, –12). P P

7. Substitution Solve the system using substitution. x – 3y = –5
2(3y – 5) + 7y = 16
If a variable is not already isolated, solve for one
variable in one of the equations. Choose to solve
for a variable with a coefficient of one,if possible.

8. Substitution x = 3y – 5 2(3y – 5) + 7y = 16 2x + 7y = 16
The solution is (1, 2).
* Be sure to check!
2(3y – 5) + 7y = 16
6y – y = 16
13y – 10 = 16
13y = 26
y = 2