In this method, the
coefficient of one of the unknowns in the two equations is made equal. After this,
the two equations are either added or subtracted depending on the sign of the
unknown whose coefficients are equated.
Example1
Solve the following
pair of simultaneous equations using the method of elimination
m + 3n = 6
and
3m
- n = 8.
Solution
Given that
m
+ 3n = 6 and 3m -
n = 8.
Step1 – number the
equations as follows
m
+ 3n = 6 …….. (equ1)
3m
- n = 8. …….. (equ2)
Step2 – multiply
equ(1) by 3 to equate the coefficients of m in both equations as follows
m
+ 3n = 6 …….. (equ1)
3*m + 3*3n = 3*6
3m + 9n = 18
…….. (equ3)
Step3 – subtract equ(2)
from equ(3) as follows
3m + 9n = 18 …….. (equ3)
3m - n = 8.
……….. (equ2)
(3m-3m) +9n –
(-n) = 18 – 8
0 + 9n + n = 10
10n =
10
n =
10 ÷ 10
n = 1
Now, substitute 1
for n in equ(2) as follows
3m - n = 8.
…….. (equ2)
3m - 1 = 8.
3m = 8 + 1 (by collecting like terms)
3m = 9
m = 9 ÷ 3
m = 3
Thus, m = 3, n = 1
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