In this chapter, you will learn to:
Solve simultaneous linear equations by the elimination method
Solve simultaneous linear equations by the substitution method
Express problems in the form of simultaneous linear equations and solve them
Solving Simultaneous Linear Equations by the Elimination Method
Example 1
Solve the simultaneous equations: 4x – 5y = 17, x – 5y = 8.
Solution
4x – 5y = 17 ----- (1)
x – 5y = 8
----- (2)
(1) - (2):
We eliminate y as the numerical
value of the coefficient of y is the
same. We subtract equation (2)
from (1) as the signs are the same
3x = 9
x=3
Substitute x = 3 into (1): 4(3) - 5y = 17
-5y = 5
y = -1
Note: x = 3 can be substituted
into equation (1) or (2) to
obtain the value of y
x = 3, y = -1.
Example 2
Solve the simultaneous equations: 3x + 2y = 8, 4x – y = 7.
Solution
3x + 2y = 8
4x – y = 7
----- (1)
----- (2)
(2) × 2:
8x - 2y = 14
----- (3)
(1) + (3):
11x = 22
x=2
Substitute x = 2 into (2): 4(2) - y = 7
8-y=7
y=1
x = 2, y = 1.
Multiply (2) by 2 to make
the coefficients of y in both
equations numerically equal
Example 3
Solve the simultaneous equations: 2x + 3y = 12, 5x – 2y = 11.
Solution
2x + 3y = 12 ----- (1)
5x – 2y = 11 ----- (2)
(1) × 2:
(2) × 3:
4x + 6y = 24 ----- (3)
15x – 6y = 33 ----- (4)
(3) + (4):
19x = 57
x=3
Substitute x = 3 into (1): 2(3) + 3y = 12
3y = 6
y=2
x = 3, y = 2.
The coefficients of y in both
equations will be numerically equal if
we multiply (1) by 2 and (2) by 3
Note: In the process of solving
simultaneous linear equations, either one
of the unknowns may be eliminated first
Page
Homework
Use the elimination method to solve the following simultaneous equations.
1. 8x + 13y = 2
5x + 13y = 11
2. 11x + 4y = 12
9x - 4y = 8
3. 7x – 3y = 15
11x – 3y = 21
4. 5x + 7y – 17 = 0
7y + 3x – 27 = 0
5. 4x – 3y = 31
16x + 5y = 39
6. 6x + 5y = 10.5
5x – 3y = -2
7. 4(2x – y + 3) = 0
2(x + y) – 3(x - y) = 6
2
Practice Questions
Use the elimination method to solve the following simultaneous equations.
1. 11x + 3y = -10
11x + 7y = 6
2. 13x + 9y = 4
17x - 9y = 26
3. 5x - 6y = 14
5x - 5y = 15
4. 3y – 2x +15 = 0
2x – 2y + 19 = 0
5. 7h – 2k = 17
3h + 4k = 17
6. 10x – 3y = 24.5
3x – 5y = 13.5
7. (x + y)/5 = (x - y)/7
3x + 17y = 2