Question

Using substitution method find the value of x and y:
$3x+5y$ $=1$ and $4x+5y$$=2$

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

Answer 1

The correct option is C $1$ and $\frac{-2}{5}$

$3x+5y=1$

$⟹3x=1-5y$

$⟹x=\frac{1-5y}{3}$

Now, Substituting $x=\frac{1-5y}{3}$ in

$4x+5y=2$

$⟹4\left(\frac{1-5y}{3}\right)+5y=2$

$⟹\frac{4-20y+15y}{3}=2$

$⟹4-5y=6$

$⟹-2=5y$

$⟹y=\frac{-2}{5}$

Substituting $y=\frac{-2}{5}$ in $x=\frac{1-5y}{3}$

$x=\frac{1-5\left(\frac{-2}{5}\right)}{3}$

$x=\frac{1+2}{3}=1$

$\therefore x=1,y=\frac{-2}{5}$