Solve: 5m-2n=12 and 2m+9n=20
5m-2n=12 —(i)
2m+9n=20 —(ii)
Multiplying equation (i) by 2 and equation (ii) by 5 we get,
10m-4n=24 —(iii)
and 10m+45n=100 —(iv)
Subtracting Equation (iii) from (iv) we get,
(10m+45n)-(10m-4n) = 100 -24
⟹ 10m +45n -10m +4n = 76
⟹ 49n = 76
⟹ n = $\frac{76}{49}$
Substituting the value of n in equation (i) we get,
$5{\mathrm{m}} – 2{\mathrm{n}} = 12$
$\Rightarrow 5{\mathrm{m}} – 2\left(\frac{76}{49}\right) = 12$
$\Rightarrow 5{\mathrm{m}} – \frac{152}{49} = 12$
$\Rightarrow 5{\mathrm{m}} = \frac{152}{49} + 12$
$\Rightarrow 5{\mathrm{m}} = \frac{152 + 588}{49}$
$\Rightarrow 5{\mathrm{m}} = \frac{740}{49}$
$\Rightarrow {\mathrm{m}} = \frac{740}{5 \times 49}$
$\Rightarrow {\mathrm{m}} = \frac{148}{49}$
Required Solution m = $\frac{148}{49}$ , n=$\frac{76}{49}$