Question

13 Select the correct answer. A system of equations and its solution are given below. System A -1 - 2y = 7 51 - 6y = -3 Solution: (-3,-2) Choose the correct option that explains what steps were followed to obtain the system of equations below. System B -x – 2y = 7 -16y = 32

Answer 1

Let's begin by listing out the information given to us:

$\begin{gathered} -x-2y=7----1 \\ 5x-6y=-3---2 \end{gathered}$

Make variable x the subject of the first equation, we have:

$\begin{gathered} -x-2y=7\Rightarrow-x=7+2y \\ -x=7+2y \\ \text{Multiply through each element by -1, we have:} \\ x=-2y-7----3 \end{gathered}$

Substitute variable x from the third equation into the second equation, we have:

$\begin{gathered} 5x-6y=-3 \\ x=-2y-7 \\ 5(-2y-7)-6y=-3\Rightarrow-10y-35-6y=-3 \\ -10y-35-6y=-3 \\ \text{Add like terms together, we have:} \\ -10y-6y=-3+35\Rightarrow-16y=32 \\ -16y=32 \end{gathered}$

Therefore, the correct answer is option C;