Question

The values of $x$ and $y$, if

$(5x-3y,y-3x)=(4,-4),$ are

• A. $(x,y)=(-2,-2)$
• B. $(x,y)=(2,-2)$
• C. $(x,y)=(2,2)$
• D. $(x,y)=(-2,2)$

Answer 1

The correct option is C $(x,y)=(2,2)$

Given that $(5x-3y,y-3x)=(4,-4)$

The ordered pairs are equal.

Thus, $5x-3y=4$ ....(1)

and $y-3x=-4\Rightarrow -3x+y=-4$ ....(2)

Multiply equation (2) by $3$, we get

$-9x+3y=-12$ ....(3)

Add equations (1) and (3), we get

$-4x=-8$

$\Rightarrow x=2$

Substitute, this value in equation (1), we get

$5\left(2\right)-3y=4$

$\Rightarrow 10-3y=4$

$\Rightarrow 6=3y$

$\Rightarrow y=2$

Therefore, the values of $(x,y)$ is $(2,2)$.