Let:
[tex]\begin{gathered} 3x-2y=8_{\text{ }}(1) \\ x+y=2_{\text{ }}(2) \end{gathered}[/tex]
Multiply (2) by 2:
[tex]2x+2y=4_{\text{ }}(3)[/tex]
Add (1) and (3):
[tex]\begin{gathered} 3x+2x-2y+2y=8+4 \\ 5x=12 \\ x=\frac{12}{5} \end{gathered}[/tex]
The error is: when the student multiply the equation (2) by 2, he only multiplied the left side of the equation by 2, but he needed to multiply the right side as well.
