Question

(2x/a)+(y/b)=2 and (x/a)-(y/b)=4 by substitution method​

Answer 1

Given:

$\frac{2x}{a} + \frac{y}{b} = 2\\\\\frac{x}{a} - \frac{y}{b} = 4$

To prove:

Find x and y by substitution method.

Solution:

$\rightarrow \frac{2x}{a} + \frac{y}{b} = 2.....(i) \\\\ \rightarrow \frac{x}{a} - \frac{y}{b} = 4....(ii)$

Solve equation (ii) and put the value in equation (i)

$\rightarrow \bold {\frac{x}{a} - \frac{y}{b} = 4}\\\\\rightarrow \frac{x}{a} = 4 +\frac{y}{b}$

Equation (i)

$\bold {\rightarrow \frac{2x}{a}+\frac{y}{b} =2}\\\\\rightarrow 2(4+\frac{y}{b})+\frac{y}{b} =2\\\\\rightarrow 8+\frac{2y}{b}+\frac{y}{b} =2\\\\\rightarrow \frac{3y}{b} =2-8\\\\\rightarrow \frac{3y}{b} =-6\\\\\rightarrow 3y =-6b\\\\\rightarrow y =-2b$

put the value of y in equation (ii):

$\rightarrow \bold{\frac{x}{a} - \frac{y}{b} =4}\\\\\rightarrow \frac{x}{a} - \frac{-2b}{b} =4\\\\\rightarrow \frac{x}{a} -(-2)=4\\\\\rightarrow \frac{x}{a} +2=4\\\\\rightarrow \frac{x}{a} =4-2\\\\\rightarrow \frac{x}{a} =2\\\\\rightarrow x= 2a$

The final value of x and y is  "2a" and "-2b".