In this method, one
of the unknowns is made the subject of the equation and its value substituted
into the other equation.
Example1
Solve the following
pair of simultaneous equations using the method of substitution.
2x
– 2y = 14 and
2x
+ y = 8.
Solution
Given that
2x
– 2y = 14 and 2x +
y = 8.
Step1 – number the
equations as follows
2x
– 2y = 14 ………. (equ1)
2x
+ y = 8 …………. (equ2)
Step 2 – make one
unknown the subject of the equation. In equation2, the coefficient of y is 1.
It is easier for us to make the y in equ2 the subject as follows
2x
+ y = 8
Subtract
2x from both sides of the equation as follows
2x
– 2x + y = 8 – 2x
y = 8 – 2x ……… (equ3)
Step3
– replace y in equ1 with “8 – 2x” in equ(1) as follows
2x
– 2y = 14 ………. (equ1)
2x
– 2(8-2x) = 14
Multiply the
content of the bracket by the coefficient of the bracket (ie 2) as follows
2x
– 2(8) -2(-2) = 14
2x
– 16 + 4x = 14
Collect like terms
2x
+ 4x = 14 + 16
6x
= 30
x
= 30 ÷ 6
x
= 5
step4 – substitute 5
for x in equ(3) above
y
= 8 – 2x ……… (equ3)
y
= 8 – 2(5)
y
= 8 – 10
y
= – 2
Thus, x = 5, y = -2
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