Question

Using substitution method find the value of x and y:
$x+4y=-4$ and $2x-3y=2$

• A. $\frac{-4}{11}$ and $\frac{-10}{11}$
• B. $\frac{-2}{11}$ and $\frac{10}{11}$
• C. $\frac{-2}{11}$ and $\frac{-10}{11}$
• D. $\frac{2}{11}$ and $\frac{-2}{11}$

Answer 1

The correct option is A $\frac{-4}{11}$ and $\frac{-10}{11}$

$x+4y=-4$ ------- (1)
$2x-3y=2$ ------ (2)
From equation 1:
$4y=-4-x$
$y=\frac{-4-x}{4}$
Substitute the value of y in equation 2:
$2x-3y=2$
$2x-3\left(\frac{-4-x}{4}\right)=2$
$8x+12+3x=8$
$11x=812$
$11x=-4$
$x=\frac{-4}{11}$
Now, Substitute $x=\frac{-4}{11}$ in equation 1:
$x+4y=-4$
$\frac{-4}{11}+4y=-4$
$-4+44y=-44$
$44y=-44+4$
$44y=-40$
$y=\frac{-40}{44}=\frac{-10}{11}$
Therefore the solution is: $x=\frac{-4}{11}$ and $y=\frac{-10}{11}$