Question

Using substitution method find the value of x and y:
$4x+9y=5$ and $-5x+3y=8$

• A. $-1$ and $\frac{-2}{5}$
• B. $-1$ and $\frac{2}{5}$
• C. $-1$ and $1$
• D. $1$ and$\frac{2}{5}$

Answer 1

The correct option is C $-1$ and $1$

$4x+9y=5$

$⟹4x=5-9y$

$⟹x=\frac{5-9y}{4}$

Substituting $x=\frac{5-9y}{4}$ in

$-5x+3y=8$, we get,

$-5\left(\frac{5-9y}{4}\right)+3y=8$

$⟹\frac{-25+45y+12y}{4}=8$

$⟹-25+45y+12y=8\times 4$

$⟹-25+57y=32$

$⟹57y=57$

$⟹y=1$

Substituting $y=1$in $x=\frac{5-9y}{4}$

$x=\frac{5-9\left(1\right)}{4}$

$⟹x=\frac{-4}{4}$

$⟹x=-1$

$\therefore x=-1,y=1$