We are given the following system of equations:
[tex]\begin{gathered} 2x+6y=14,(1) \\ x-6y=-20,(2) \end{gathered}[/tex]To solve the system we will use the method of elimination. We will add equations (1) and (2) so that the variable "y" gets canceled out, like this:
[tex]2x+6y+x-6y=14-20[/tex]Adding like terms:
[tex]3x=-6[/tex]Now, we divide both sides by 3:
[tex]x=-\frac{6}{3}=-2[/tex]Therefore, the value of "x" is -2. Now, we determine the value of "y" by substituting the value if "x" in equation (1):
[tex]-2-6y=-20[/tex]Now, we add 2 to both sides:
[tex]\begin{gathered} -6y=-20+2 \\ -6y=18 \end{gathered}[/tex]Now, we divide both sides by -6:
[tex]y=\frac{18}{-6}=-3[/tex]Therefore, the solution of the system is:
[tex]\begin{gathered} x=-2 \\ y=-3 \end{gathered}[/tex]