Solve 3x+4y=25 and 5x-6y=-9 by Elimination and Substitution Method

Elimination Method

3x+4y=25 —-(i)

5x-6y=-9 —-(ii)

Multiplying Equation (i) by 3 and Equation (ii) by 2 we get,

9x +12y = 75 —-(iii)

and 10x -12y= -18 —-(iv)

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

(9x +12y)+(10x -12y)=75+(-18)

⟹ 9x +12y +10x -12y = 75-18

⟹ 19x = 57

⟹ x = $\frac{57}{19}$

⟹ x = 3

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

3(3)+4y=25

⟹ 9+4y=25

⟹ 4y=25-9

⟹ 4y =16

⟹y= $\frac{16}{4}$

⟹ y= 4

Required Solution x=3 , y=4.

3x+4y=25 —-(i)

5x-6y=-9 —-(ii)

From Equation (i) we get,

3x= 25-4y

$\Rightarrow x = \frac{25 – 4y}{3}$ —(iii)

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

$5{\mathrm{x}} – 6{\mathrm{y}} = – 9$

$\Rightarrow 5\left(\frac{25 – 4y}{3}\right) – 6{\mathrm{y}} = – 9$

$\Rightarrow \frac{125 – 20{\mathrm{y}}}{3} – 6{\mathrm{y}} = – 9$

$\Rightarrow \frac{125 – 20{\mathrm{y}} – 18{\mathrm{y}}}{3} = – 9$

$\Rightarrow 125 – 38{\mathrm{y}} = – 27$

$\Rightarrow 125 + 27 = 38{\mathrm{y}}$

$\Rightarrow 38{\mathrm{y}} = 152$

$\Rightarrow {\mathrm{y}} = \frac{152}{38}$

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

From Equation (iii) we get,

${\mathrm{x}} = \frac{25 – 4{\mathrm{y}}}{3}$

$\Rightarrow {\mathrm{x}} = \frac{25 – 4(4)}{3}$

$\Rightarrow {\mathrm{x}} = \frac{25 – 16}{3}$

$\Rightarrow {\mathrm{x}} = \frac{9}{3}$

$\Rightarrow {\mathrm{x}} = 3$

Required Solution x=3 , y=4.