Name
May 16, 2013
Geometry
“Solving systems: substitution method” page 1
Solving systems: substitution method
The substitution method is a way to solve a system of two equations algebraically. Its steps are:




Solve one of the equations for either x or y (your choice of which equation and
which variable — try to choose whichever solving is going to be easiest).
Take the result of the solving, and substitute into the other equation.
You should now have a one-variable equation. Solve for that variable.
Use one of the original equations, put in the just-found number for one variable,
and solve for the other variable.
Example
To check your solution, verify that it makes both of the equations true.
=1
2x – 3y = 12
3 + (–2) = 1
2(3) – 3(–2) = 12
x + y
1
=1
6 – (–6) = 12
12
= 12
Name
May 16, 2013
Geometry
“Solving systems: substitution method” page 2
Practice problems
Directions: Solve each system of equations using the substitution method. Check your solutions.
1. 3x – y = –15, 2x + y = 0
Solve
Check
2. –2x + 4y = 6, 3x – y = 1
Solve
Check
3. x – 5y = 18, 2x – 3y = –13
Solve
Check
4. y = x – 4, 3x = –8 + y
Solve
Check
Name
May 16, 2013
Geometry
“Solving systems: substitution method” page 3
5. y = x + 3, 7x + y = -1
Solve
Check
6. 4x + y = 12, y = –8
Solve
7. –3x = 9,
Solve
Check
2x + y = –13
Check
Name
May 16, 2013
Geometry
“Solving systems: substitution method” page 4
Word problems
Directions for problems 8–9: Solve these word problems using the substitution method.
8. For Thanksgiving, the Adams family is having a potluck dinner. Each person attending
brings either 1 dish or 2 dishes. In total, 14 people come to the dinner, and there are 23 dishes.
How many people brought 1 dish and how many people brought 2 dishes?
Variables
x = # of people that brought 1 dish
y = # of people that brought 2 dishes
a. System
b. Solve
d. Answer
c. Check
(full sentence relating to the problem context)
9. A community center serves a large Thanksgiving dinner for people in need. 100 people
attend the dinner, and 80 pounds of turkey are eaten. The organizers estimate that each adult
eats 1 pound of turkey and each child eats 12 pound of turkey. How many adults and how
many children attended the dinner?
a. Variables
x = ______________________
y = ______________________
b. System
c. Solve
e. Answer
d. Check
(full sentence relating to the problem context)