Solve 17x+10y=118 and 15x-6y=30 by Elimination and Substitution Method

Elimination Method

17x+10y=118 —(i)

15x-6y=30 —(ii)

Multiplyong Equation (i) by 3 and Equation (ii) by 5 we get,

51x+30y=354 —(iii)

75x-30y = 150 —(iv)

Adding Equations (iii) and (iv) we get,

51x+30y + 75x-30y = 354+ 150

⟹ 126x = 504

⟹ x = $\frac{504}{126}$

⟹ x = 4

Substituting the value of x in equation (i) we get,

17(4) +10y = 118

⟹ 68 +10y=118

⟹ 10y=118-68

⟹ 10y=50

⟹ y = $\frac{50}{10}$

⟹ y = 5

Required Solutions are x = 4 , y=5

17x+10y=118 —(i)

15x-6y=30 —(ii)

From Equation (i) we get,

$17x + 10y = 118$

$\Rightarrow 17x = 118 – 10y$

$\Rightarrow x = \frac{118 – 10y}{17}$ —(iii)

Substituting the value of x in equation (ii) we get,

$15{\mathrm{x}} – 6{\mathrm{y}} = 30$

$\Rightarrow 15\left(\frac{118 – 10y}{17}\right) – 6{\mathrm{y}} = 30$

$\Rightarrow \frac{1770 – 150{\mathrm{y}}}{17} – 6{\mathrm{y}} = 30$

$\Rightarrow \frac{1770 – 150{\mathrm{y}} – 102{\mathrm{y}}}{17} = 30$

$\Rightarrow 1770 – 252{\mathrm{y}} = 510$

$\Rightarrow 1770 – 510 = 252{\mathrm{y}}$

$\Rightarrow 1260 = 252{\mathrm{y}}$

$\Rightarrow {\mathrm{y}} = \frac{1260}{252}$

$\Rightarrow {\mathrm{y}} = 5$

From Equation (iii) we get,

${\mathrm{x}} = \frac{118 – 10{\mathrm{y}}}{17}$

$\Rightarrow {\mathrm{x}} = \frac{118 – 10(5)}{17}$

$\Rightarrow {\mathrm{x}} = \frac{118 – 50}{17}$

$\Rightarrow {\mathrm{x}} = \frac{68}{17}$

$\Rightarrow {\mathrm{x}} = 4$

Required Solutions are x = 4 , y=5