11x+15y+23=0,7x-2y-20=0 solve it elimination method

The given system of equations is
11x + 15y + 23 = 0 ....(1)
7x - 2y - 20 = 0 ....(2)
To solve the equations (1) and (2) by cross multiplication method,
we draw the diagram below:

Then,
{tex}\Rightarrow \;\frac{x}{{(15)( - 20) - ( - 2)(23)}} = \frac{y}{{(23)(7) - ( - 20)(11)}}{/tex}{tex}= \frac{1}{{(11)( - 2) - (7)(15)}}{/tex}
{tex}\Rightarrow \;\frac{x}{{ - 300 + 46}} = \frac{y}{{161 + 220}} = \frac{1}{{ - 22 - 105}}{/tex}
{tex}\Rightarrow \;\frac{x}{{ - 254}} = \frac{y}{{381}} = \frac{1}{{ - 127}}{/tex}
{tex}\Rightarrow \;x=\frac{{ - 254}}{{ - 127}} = 2{/tex} and {tex}y = \frac{{381}}{{ - 127}} = - 3{/tex}
Hence, the required solution of the given pair of equations is
x = 2, y = -3
Verification : substituting x = 2, y = -3,
We find that both the equations (1) and (2) are satisfied as shown below:
11x + 15y + 23 = 11(2) + 15(-3) + 23
= 22 - 45 + 23 = 0
7x - 2y - 20 = 7(2) - 2(-3) - 20
= 14 + 6 - 20 = 0
Hence, the solution we have got is correct.