Question

Solve
$6x-3y+10=0$
$2x-3y+9=0$

Answer 1

$6x-3y+10=0$ .......$\left(1\right)$

$2x-3y+9=0$ .......$\left(2\right)$

By the method of elimination,

$2\times$eqn$\left(1\right)-6\times$eqn$\left(2\right)$ we get

$12x-6y+20-12x+18y-54=0$

$\Rightarrow 12y-34=0$

$\Rightarrow y=\frac{34}{12}=\frac{17}{6}$

Substitute $y=\frac{17}{6}$ in $\left(1\right)$ we get

$6x-3\times \frac{17}{6}+10=0$

$\Rightarrow 6x=\frac{17}{2}-10=\frac{17-20}{2}=\frac{-3}{2}$

$\therefore x=\frac{17}{6},y=\frac{-3}{2}$