Solve: 5m-2n=12 and 2m+9n=20

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=$\frac{76}{49}$

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