Question

Given, $3x+4y=-23$ and $2y-x=-19$
What is the solution $(x,y)$ to the system of equations above?

• A. $(-5,-2)$
• B. $(3,-8)$
• C. $(4,-6)$
• D. $(9,-6)$

Answer 1

Answer: (B)

$(3,-8)$

Let $3x+4y=-23...\left(1\right)$
and $-x+2y=-19...\left(2\right)$
Multiplying equation $\left(2\right)$ with $3$, we get
$-3x+6y=-57...\left(3\right)$
Adding equations $\left(1\right)$ and $\left(3\right)$, we get
$10y=-80$
$\Rightarrow y=-8$
Substituting $y=-8$ in equation $\left(2\right)$, we get
$-16-x=-19$
$\Rightarrow x=3$
Hence, the solution of the given two equations is $(3,-8)$