Simultaneous equations – elimination method


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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