Question

Solve the following simultaneous equation.

5m – 3n = 19; m – 6n = –7

Answer 1

5m – 3n = 19                  ...(I)
m – 6n = –7                    ...(II)

Multiply equation (I) by 2, we get,
10m – 6n = 38                ...(III)

Subtracting (II) from (III), we get,

\[\begin{array}{l}  
\phantom{\texttt{0}}\texttt{10m – 6n = 38}\\ \phantom{\texttt{}}\texttt{– m – 6n = –7}\\ \hline\phantom{\texttt{}}\texttt{(-) (+) (+)}\\ \hline \end{array}\]
∴ 9m = 45

∴ m = `45/9`

∴ m = 5

Putting the value of m = 5 in equation (II), we get,
m – 6n = –7
∴ 5 – 6n = –7
∴ – 6n = –7 – 5
∴ – 6n = –12

∴ n = `(–12)/(– 6)`

∴ n = 2
Thus, (m, n) = (5, 2).