1. Solving Systems by Elimination
5-3
Solving Systems by Elimination
Lesson Presentation
Lesson Quiz
Holt McDougal Algebra 1
Holt Algebra 1

2. Warm Up /14/16
Simplify each expression.
1. 3x + 2y – 5x – 2y
2. 5(x – y) + 2x + 5y
Write the least common multiple. 3.
3 and 6 4.
4 and 10

3. Essential Objectives
Solve systems of linear equations in two variables by elimination.
Compare and choose an appropriate method for solving systems of linear equations.

4. Solving Systems of Equations by Elimination
Step 1
Write the system so that like terms are aligned.
Step 2
Eliminate one of the variables and solve for the other variable.
Step 3
Substitute the value of the variable into one of the original equations and solve for the other variable.
Write the answers from Steps 2 and 3 as an ordered pair, (x, y), and check.
Step 4

5. Example: Elimination Using Addition
3x – 4y = 10
Solve by elimination.
x + 4y = –2
Step 1
3x – 4y = 10
x + 4y = –2
Step 2
4x = 8
4x = 8
4x = 8
x = 2

6. Example Continued
Step 3
x + 4y = –2
Write one of the original equations.
2 + 4y = –2
Substitute 2 for x.
– –2
4y = –4
Subtract 2 from both sides.
4y –4
y = –1
Step 4 (2, –1)

7. Example
y + 3x = –2
Solve by elimination.
2y – 3x = 14
Step 1
2y – 3x = 14
y + 3x = –2
Step 2
3y = 12
3y = 12
y = 4

8. Example Continued
Write one of the original equations.
Step 3 y + 3x = –2
4 + 3x = –2
Substitute 4 for y.
– –4
3x = –6
Subtract 4 from both sides.
3x = –6
x = –2
Step 4
(–2, 4)

9. Example: Elimination Using Subtraction
2x + y = –5
Solve by elimination.
2x – 5y = 13
2x + y = –5
Step 1
–(2x – 5y = 13)
2x + y = –5
–2x + 5y = –13
0 + 6y = –18
Step 2
Eliminate x.
6y = –18
y = –3

10. Example Continued
Write one of the original equations.
Step 3
2x + y = –5
2x + (–3) = –5
Substitute –3 for y.
2x – 3 = –5
2x = –2
x = –1
Step 4
(–1, –3)

11. In some cases, you will first need to multiply one or both of the equations by a number so that one variable has opposite coefficients.

12. Example: Elimination Using Multiplication First
Solve the system by elimination.
x + 2y = 11
–3x + y = –5
Multiply each term in the second equation by –2 to get opposite y-coefficients.
x + 2y = 11
Step 1
–2(–3x + y = –5)
x + 2y = 11
+(6x –2y = +10)
7x = 21
Step 2
7x = 21
x = 3
Solve for x.

13. Example Continued
Write one of the original equations.
Step 3
x + 2y = 11
3 + 2y = 11
Substitute 3 for x.
– –3
2y = 8
Subtract 3 from both sides.
y = 4
Step 4
(3, 4)

15. Lesson Quiz
Solve each system by elimination. 1. 2. 3.
Show your work for full credit!!!
2x + y = 25
(11, 3)
3y = 2x – 13
–3x + 4y = –18
(2, –3)
x = –2y – 4
–2x + 3y = –15
(–3, –7)
3x + 2y = –23