Question

Which ordered pair is the solution to the system of equations? {x+3y=−12y=13x−6?

Answer 1

The solution of the system is: $( \frac{3}{20}, -\frac{81}{20})$

Explanation

Given system of equations is...

$x+3y= -12 .....................................(1)\\\\\\ y=13x-6 ........................................(2)$

Here we will use substitution method as $y$ is already isolated in equation (2). So, substituting $y= 13x-6$ into equation (1) , we will get...

$x+3y =-12\\\\ x+3(13x-6)=-12\\\\ x+39x -18 =-12\\\\ 40x -18 = -12\\\\ 40x =-12+18\\\\ 40x = 6\\\\ x =\frac{6}{40} =\frac{3}{20}$

Plugging the value $x=\frac{3}{20}$ into equation (2)....

$y= 13x -6\\\\ y= 13(\frac{3}{20}) -6\\\\ y=\frac{39}{20} -6\\\\ y=\frac{39-120}{20}=-\frac{81}{20}$

So, the solution of the system is: $( \frac{3}{20}, -\frac{81}{20})$