Question

If $2x_{1}x-3y_{1}y=2x_1^2-3y_1^2\&4x-3y=5$ are equation of same line, find the value of $x_1+y_1$.

Answer 1

Given equation of line

$2x_{1}x-3y_{1}y=2x_1^2-3y_1^2$ ..............(1)

$4x-3y=5$ ..............(2)

Both equation (1) $\&$ (2) represent same line ratio of their coefficients must be same

$\therefore \frac{2x_1}{4}=\frac{3y_1}{3}=\underset{}{\frac{2x_1^2-3y_1^2}{5}=k}$ (Let's say)

$\Rightarrow x_1=\frac{4k}{2}=2k$

$y_1=k$

$\frac{2x_1^2-3y_1^2}{5}=k$

$\frac{2(2k{)}^2-3(k{)}^2}{5}$

$2\times 4k^2-3k^2=5k$

$8k-3k=5$

$5k=5$

$k=1$

Then $x_1=2\times 1=2$

and $y_1=1$

$x_1+y_1=2+1=3$