Question

If $-2x=4y+6$ and $2(2y+3)=3x-5$, what is the solution $(x,y)$ to the system of equations above?

Answer 1

The given set of equations are,

$-2x=4y+\mathrm{6.....}\left(i\right)$

and $2\left(2y+3\right)=3x-\mathrm{5.......}\left(ii\right)$

from (i)

$-2x=4y+6$

$\Rightarrow 2x+4y=-\mathrm{6......}\left(iii\right)$

And,from (ii)

$2\left(2y+3\right)=3x-5$

$\Rightarrow 4y+6=3x-5$

$\Rightarrow 3x-4y=\mathrm{11.......}\left(iv\right)$

adding (iii) and (iv)

$5x=5$

$\Rightarrow x=1$

from (iii)

$2\times 1+4y=-6$

$\Rightarrow 2+4y=-6$

$\Rightarrow 4y=-8$

$\Rightarrow y=-2$

Therefore, the solution to the given system of the equations is $\left(1,-2\right)$.