Answer :
Given the system
[tex]\begin{gathered} 2x+y=4 \\ 6x-2y=6 \end{gathered}[/tex]First step, the first equation is multiplied by -3
[tex]\begin{gathered} -3(2x+y)=-3\cdot4 \\ -3\cdot2x-3\cdot y=-12 \\ -6x-3y=-12 \end{gathered}[/tex]Step 2, add both equations, you have to add the like terms
[tex]\begin{gathered} (-6x-3y)+(6x-2y)=-12+6 \\ -6x+6x-3y-2y=-12+6 \\ 0x-5y=-6 \\ -5y=-6 \end{gathered}[/tex]Step 3 divide both sides by -5 to determine the value of y
[tex]\begin{gathered} -\frac{5y}{-5}=-\frac{6}{-5} \\ y=\frac{6}{5} \end{gathered}[/tex]Step 4 determine the value of x, by replacinf y=6/5 in the first equation
[tex]\begin{gathered} 2x+y=4 \\ 2x+\frac{6}{5}=4 \\ 2x=4-\frac{6}{5} \\ 2x=\frac{14}{5} \\ \frac{2x}{2}=\frac{\frac{14}{5}}{2} \\ x=\frac{14}{5}\cdot\frac{1}{2} \\ x=\frac{7}{5} \end{gathered}[/tex]Solution (7/5, 6/5)
The error is in step 3, (-3y)+(-2y)=-5y NOT -y