Respuesta :
The solution of the system is: [tex] ( \frac{3}{20}, -\frac{81}{20}) [/tex]
Explanation
Given system of equations is...
[tex] x+3y= -12 .....................................(1)\\\\\\ y=13x-6 ........................................(2) [/tex]
Here we will use substitution method as [tex] y [/tex] is already isolated in equation (2). So, substituting [tex] y= 13x-6 [/tex] into equation (1) , we will get...
[tex] 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} [/tex]
Plugging the value [tex] x=\frac{3}{20} [/tex] into equation (2)....
[tex] y= 13x -6\\\\ y= 13(\frac{3}{20}) -6\\\\ y=\frac{39}{20} -6\\\\ y=\frac{39-120}{20}=-\frac{81}{20} [/tex]
So, the solution of the system is: [tex] ( \frac{3}{20}, -\frac{81}{20}) [/tex]
