Question

Solve the equations $2x-3y=1$ and $x+2y=-3$ by the method of elimination

Answer 1

Let us Solve the equations $2x-3y=1$ and $x+2y=-3$ by the method of elimination

$2x-3y=1$ ......$\left(1\right)$

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

Multiply eqn$\left(1\right)$ by $1$ and eqn$\left(2\right)$ by $2$

$2x-3y=1$ ......$\left(3\right)$

$2x+4y=-6$ ......$\left(4\right)$

Equation $\left(3\right)-\left(4\right)$

$2x-3y-2x-4y=1-(-6)$

$\Rightarrow -7y=1+6=7$

$\therefore y=\frac{7}{-7}=-1$

Substituting the value of $y=-1$ in eqn$\left(1\right)$ we get

$2x-3\times -1=1$

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

Hence the co-ordinates are $(-1,-1)$ lies in third quadrant.