Question

2x+3y=9 4x+6y=18 by substitution method​

Answer 1

$\huge {x = \frac{9 - 3y}{2}}$

Step-by-step explanation:

Here,

2x + 3y = 9

=> 2x + 3y - 9 = 0...(i)

4x + 6y = 18

=> 4x + 6y - 18 = 0....(ii)

$a_{1} = 2, b_{1} = 3, c_{1} = -9 \\ a_{2} = 4, b_{2} = 6, c_{2} = -18 \\ \\ so, \\ \frac{a_{1}}{a_{2}} = \frac{2}{4} = \frac{1}{2} \\ \frac{b_{1}}{b_{2}} = \frac{3}{6} = \frac{1}{2} \\ \frac{c_{1}}{c_{2}} = \frac{-9}{-18} = \frac{1}{2} \\ \\ \implies \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

So there will be indefinite values of x and y.

$2x + 3y = 9 \\ \implies 2x = 9 - 3y \\ \implies x = \frac{9-3y}{2}$

So if we take any value of y, value of x will be (9-3y)/2

hope it helps.