Question

Solve the following systems of equations:$11x+15y+23=0$

$7x-2y-20=0$

Answer 1

Given pair of linear equations: $11x+15y+23=\mathrm{0...}\left(1\right)$ and $7x-2y-20=\mathrm{0...}\left(2\right)$

Now, Multiply $\left(1\right)$ by $2$ and $\left(2\right)$ by $15$

$\Rightarrow 2(11x+15y+23=0)=22x+30y+46=\mathrm{0...}\left(3\right)$ and

$\Rightarrow 15(7x-2y-20=0)=105x-30y-300=\mathrm{0...}\left(4\right)$

Using the method of Elimination, add equation $\left(3\right)$ and $\left(4\right)$

$\Rightarrow (22x+30y+46=0)+(105x-30y-300=0)$

$\Rightarrow 127x=254$

$\Rightarrow x=\frac{254}{127}=2$

Putting the value if $x$ in $\left(1\right)$, we get,

$\Rightarrow 11\left(2\right)+15y+23=0$

$\Rightarrow 15y=-45$

$\Rightarrow y=-3$

Hence, $x=2$ and $y=-3$