1. Solving Systems of Linear Equations by Elimination
Chapter 1 Systems of Equations
1.5
Solving Systems
of Linear Equations
by Elimination
MATHPOWERTM 11, WESTERN EDITION
1.5.1

2. Elimination Method- Principles
When using elimination to solve a linear system,
the equations are combined to eliminate one of
the variables.
Multiplying both sides of an equation by
the same constant does not change the equation.
Adding or subtracting the equations of a
linear system does not change the solution.
1.5.2

3. numerical coefficients of the x- or y-terms must be
Solve by Elimination
Solve: x + 2y = 11 (1)
To use elimination, the
numerical coefficients of
the x- or y-terms must be
the same or opposite.
The numerical coefficients of the
y-terms have opposite values,
Therefore, the equations can be
added to eliminate the y-terms.
Then, solve for x.
3x - 2y = 9 (2)
4x = 20
x = 5
x + 2y = 11 (1)
5 + 2y = 11
2y = 6
y = 3
Substitute to solve for
the second variable.
3x - 2y = 9 (2)
3(5) - 2(3) = 9
= 9
9 = 9
Check your solution in
the second equation.
The solution is (5, 3).
1.5.3

4. When the coefficients are not the same or opposite,
Solve by Elimination
Solve: 3x + 2y = 12 (1)
x 2
When the coefficients are
not the same or opposite,
multiply one, or both
equations by a constant.
6x + 4y = (1)
2x + 3y = 13 (2)
x 3
6x + 9 y = (2)
-5y = -15
y = 3
3x + 2y = (1)
3x + 2(3) = 12
3x + 6 = 12
3x = 6
x = 2
2x + 3y = 13 (2)
2(2) + 3(3) = 13
4 + 9 = 13
13 = 13
Therefore, the
solution is (2, 3).
1.5.4

5. Therefore, the solution is (0, -2).
Solve by Elimination
x - 3y = (1)
Solve :
x = 6 + 3y (1)
3(x - 2) = 4 + 2(y - 3) (2)
3x - 6 = 4 + 2y – 6 (2)
3x - 2y = (2)
3x - 9y = 18 (1)
3x - 2y = 4 (2)
3x - 2y = (2)
3x - 2(-2) = 4
3x = 0
x = 0
Check:
x - 3y = (1)
0 - 3(-2) = 6
6 = 6
-7y = 14
y = -2
Therefore, the solution is (0, -2).
1.5.5

6. Assignment Suggested Questions: Pages 38-40 1-13, 17-33 odd, 43, 44
1.5.6