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Solve the following simultaneous linear equations by using
elimination method. The steps for solving
simultaneous linear
(a) x + 2y = 9 and 3x – 2y = 15 equations in two variables
(b) 2x + 5y = 14 and 3x + 4y = 7 using elimination method:

Multiply one or both
(a) x + 2y = 9 .…… 1 Identify the variable with equations with a
3x – 2y = 15 …… 2 the same coefficient. number so that the
coefficient of one of
1 + 2 : 4x + 0 = 24 Eliminate the variable y by the variables is equal.
adding 1 and 2.
4x = 24
x = 6 Add or subtract both
the equations to
Substitute x = 6 into 1.
6 + 2y = 9 eliminate one of
the variables.
2y = 9 – 6 CHAPTER
2y = 3
Solve the linear
3 6
y = equation in
2 one variable.
3
Thus, x = 6 and y = .
2
Substitute the value
(b) 2x + 5y = 14 …… 1 • Multiply 1 and 2 to obtained into the
3x + 4y = 7 …… 2 equate the coefficient original equation to
find the value of the
1 × 3 : 6x + 15y = 42 …… 3 of x. other variable.
2 × 2 : 6x + 8y = 14 …… 4 • The LCM for 2 and 3 is 6.

3 – 4 : 0 + 7y = 28 Eliminate the variable x by
7y = 28 subtracting 4 from 3. Scan the QR Code or
y = 4 visit https://youtu.
be/L0DJskZw3y0
Substitute y = 4 into 1. to learn about the
2x + 5(4) = 14 solution of Example
2x + 20 = 14 13(b) by using
2x = 14 – 20 scientific calculator.
2x = – 6
x = –3
Thus, x = –3 and y = 4.

Self Practice 6.3b

1. Solve the following simultaneous linear equations:
(a) y = 3x + 1 (b) x + y = 5
x + 2y = 16 2x – y = 22
(c) 4x + 3y = 8 (d) 8x + 3y = – 4
x – 3y = 2 5x + 2y = 6

141
Linear Equations

06 TB Math F1.indd 141 11/10/16 12:15 PM