Question

Solve for $x$ and $y:$ $152x-378y=-74,-378x+152y=-604.$

• A. $x=-2$ and $y=-1$
• B. $x=2$ and $y=41$
• C. $x=2$ and $y=1$
• D. $x=-2$ and $y=1$

Answer 1

The correct option is C $x=2$ and $y=1$

$152x-378y=-74\dots \dots \left(i\right)$

$-378x+152y=-604\dots \dots \left(ii\right)$

On adding equation $\left(i\right)$ and $\left(ii\right),$ we get

$152x-378y+(-378x+152y)=-74+(-604)$

$\Rightarrow -226x-226y=-678$

$\Rightarrow x+y=3\dots \dots \left(iii\right)$

On subtracting equation $\left(i\right)$ from $\left(ii\right),$ we get

$-378x+152y-(152x-378y)=-604+74$

$\Rightarrow -530x+530y=-530$

$\Rightarrow x-y=1\dots \dots \left(iv\right)$

On adding equation $\left(iii\right)$ and $\left(iv\right),$ we get

$x+y+x-y=3+1$

$\Rightarrow 2x=4$

$\Rightarrow x=2$

And, $x+y=3$

$\Rightarrow y=1$