Question

A student solved a system of equations by elimination. The answer is not correct. Describe the error in the solution.Original Problem:3−2=8+=2Student Work:3−2=82+2=25=10=2

Answer 1

Let:

$\begin{gathered} 3x-2y=8_{\text{ }}(1) \\ x+y=2_{\text{ }}(2) \end{gathered}$

Multiply (2) by 2:

$2x+2y=4_{\text{ }}(3)$

Add (1) and (3):

$\begin{gathered} 3x+2x-2y+2y=8+4 \\ 5x=12 \\ x=\frac{12}{5} \end{gathered}$

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.