Question

Calculate the value of $x+y$ in the system of equations shown above.

$3x+4y=12$ and $4x+3y=-5$

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is D $1$

Let $3x+4y=12$.....(1)

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

Multiply (1) by $3$ and (2) by $4$, we get

$\Rightarrow 9x+12y=36$..........(3)

$\Rightarrow 16+12y=-20$..........(4)

On subtracting equations (3) and (4), we get

$\Rightarrow -7x=56$

$\Rightarrow x=\frac{56}{-7}=-8$

Put the value of $x=-8$ in (1)

$\Rightarrow 3(-8)+4y=12$

$\Rightarrow -24+4y=12$

$\Rightarrow 4y=12+24$

$\Rightarrow 4y=36$

$\Rightarrow y=\frac{36}{4}=9$

$\therefore x+y=-8+9=1$