Advanced Math
Solving Systems Review
Substitution and Elimination
Name:
May 2015
Substitution Method:
1. _________________ one of the equations for one of its variables.
2. _________________ this expression into the other equation and solve for the other variable.
3. _________________ this value into the revised first equation and solve for the other variable.
4. _________________ the solution by plugging it into each of the original equations.
Example 1: Solve the linear systems using the substitution method.
a.
𝑥 − 2𝑦 = 4
2𝑥 − 3𝑦 = 1
b.
−2𝑥 + 𝑦 = 8
3𝑥 + 𝑦 = −2
When you use the substitution method, you will obtain the same solution (𝑥, 𝑦) whether you solve for 𝑥
or for 𝑦 first. You should begin solving for the variable that has a _________________________________.
Example 2: Fill in the blank to indicate which variable you should solve for first.
a.
5𝑥 − 3𝑦 = 2
𝑥 + 2𝑦 = 3
b.
−4𝑥 + 𝑦 = 0
2𝑥 − 3𝑦 = −10
Solve for _____ first here.
Solve for _____ first here.
If neither variable has a coefficient of 1 then you can use the _____________________________ method.
Elimination Method:
1. _______________________the equations with like terms in columns.
2. _______________________________________ that differ only in sign by multiplying each term of
one or both equations by the appropriate number.
3. _________________________ and solve for the remaining variable.
4. ____________________ the solution by plugging it into each of the original equations.
Example 3: Solve the linear systems using the elimination method.
a.
3𝑥 + 2𝑦 = 10
−3𝑥 + 3𝑦 = 15
c.
3𝑥 − 2𝑦 = 5
−6𝑥 + 4𝑦 = 7
b.
5𝑥 + 4𝑦 = 6
−2𝑥 − 3𝑦 = −1
Advanced Math
Solving Systems Review
Substitution and Elimination
Name:
May 2015
Solve each system using substitution or elimination.
1.
𝑦 = 3𝑥
2.
𝑥 + 𝑦 = 4
𝑥 = ________
3.
7𝑥 – 2𝑦 = 11
𝑦 = ________
𝑥 + 4𝑦 = −8
𝑥 = ________
4.
𝑥 – 4𝑦 = −8
𝑥 = ________
5.
𝑦 = ________
𝑦 = ________
2𝑥 – 3𝑦 = 1
5𝑥 + 4𝑦 = 14
𝑥 = ________
2𝑥 + 5𝑦 = 3
𝑥 = ________
6.
3𝑦 = 2𝑥 + 12
7.
𝑦 = ________
−𝑥 + 3𝑦 = −7
2𝑥 – 5𝑦 = −16
𝑥 = ________
5𝑥 − 𝑦 = 10
𝑦 = ________
𝑦 = ________
4𝑥 + 3𝑦 = 180
𝑥 – 𝑦 = 10
𝑥 = ________
8.
𝑦 = ________
2𝑥 + 3𝑦 = 9
3𝑥 + 2𝑦 = 12
𝑥 = ________
𝑦 = ________
Solve each system using substitution or elimination.
9.
0.7𝑥 + 0.5𝑦 = 2.9
2.1𝑥 – 2.5𝑦 = −3.3
𝑥 = ________
𝑦 = ________
10.
𝑥 – 4𝑦 = 11
5𝑥 – 7𝑦 = −10
𝑥 = ________
𝑦 = ________
For #11-13, set up a system of 2 equations and solve. Use either substitution or elimination.
11.
The sum of two numbers is 17 and their difference is 29. Find the numbers.
12.
Adult tickets for the school musical sold for $3.50 and student tickets sold for $2.50. Three
hundred twenty-one tickets were sold altogether for $937.50. How many of each kind of ticket
were sold?
13.
Two complementary angles differ by 48˚. What are the angles?