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Solve Linear
Systems by
Elimination
February 3, 2014
Pages 444-446
7.3 SOLVING SYSTEMS BY
ELIMINATION
Students will be able to:
Solve systems of linear equations in
two variables by elimination.
Compare and choose an appropriate
method for solving systems of linear
equations.
1. Solve the linear system by elimination.
SOLUTION
STEP 1
STEP 2
STEP 3
ANSWER
2x + 3y = 11
– 2x + 5y = 13
Equation 1
Equation 2
Add the equations to
eliminate one variable.
Solve for y.
2x + 3y = 11
– 2x +5y = 13
8y = 24
y=3
Substitute 3 for y in either equation and
Solve for x.
2x + 3y = 11
2x + 3(3) = 11
x=1
The solution is (1, 3).
Write Equation 1
Substitute 3 for y.
Solve for x.
2. Solve the linear system by elimination.
8x – 4y = –4
Equation 1
SOLUTION
4y = 3x + 14
Equation 2
STEP 1
STEP 2
STEP 3
STEP 4
ANSWER
Rewrite Equation 2 in standard form.
8x – 4y = –4
8x – 4y = –4
4y = 3x + 14
3x + 4y = 14
5x
= 10
Add the equations.
Solve for x.
x=2
Substitute 2 for x in either equation and
solve for y.
4y = 3x + 14
Write Equation 2.
Substitute 2 for x.
4y = 3(2) + 14
y=5
Solve for y.
The solution is (2, 5).
3. Solve the linear system by elimination.
SOLUTION
STEP 1
STEP 2
4x – 3y = 5
– 2x + 3y = – 7
Add the equations to
eliminate one variable.
Solve for x.
STEP 3
Equation 1
Equation 2
4x – 3y = 5
– 2x +3y = – 7
2x = – 2
x=–1
Substitute – 1 for x in either equation and
Solve for x.
Write Equation 1.
4x – 3y = 5
2(– 1) – 3y = 5
Substitute – 1 for x.
y=–3
Solve for x.
ANSWER
The solution is (– 1, – 3).
4. Solve the linear system by elimination.
SOLUTION
STEP 1
STEP 2
STEP 3
– 5x – 6y = 8
5x + 2y = 4
Equation 1
Equation 2
– 5x – 6y = 8
5x + 2y = 4
– 4y = 12
y=–3
Substitute – 3 for y in either equation and solve
for y.
Add the equations to
eliminate one variable.
Solve for y.
– 5x – 6y = 8
– 5x – 6(–3) = 8
x=2
ANSWER
The solution is (2, -3).
Write Equation 1.
Substitute – 3 for y.
Solve for x.
5. Solve the linear system by elimination.
6x – 4y = 14
SOLUTION
– 3x + 4y = 1
STEP 1 Add the equations to
eliminate one variable.
STEP 2 Solve for x.
Equation 1
Equation 2
6x – 4y = 14
– 3x + 4y = 1
3x
= 15
x
= 5
STEP 3 Substitute 5 for x in either equation and solve
for y.
Write Equation 1.
6x – 4y = 14
Substitute 5 for x.
6(5) – 4y = 14
Solve for y.
y=4
ANSWER
The solution is (5, 4).
6. Solve the linear system by elimination.
SOLUTION
2x + 5y = 12
5y = 4x + 6
Equation 1
Equation 2
STEP 1
Rewrite Equation 2 so that the like terms are
arranged in columns.
2x + 5y = 12
2x + 5y = 12
5y = 4x + 6
– 4x + 5y = 6
STEP 2
Subtract the equations.
STEP 3
Solve for x.
6x
= 6
x=1
STEP 4
Substitute 1 for x in either equation and
solve for y.
2x + 5y = 12
2(1) + 5y = 6
x= 2
Write Equation 2.
Substitute 1 for x.
Solve for y .
ANSWER
The solution is (1, 2).
HOMEWORK
PAGE 447, # 4-22, EVEN