Question

Determine whether the ordered pair is the solution to the system

$$\begin{gathered} x-3y=-8 \\ -3x-y=4 \end{gathered}$$

(a)$(2,-2)$

(b)$(-2,2)$

Short answer

$(2,-2)$does not make both equations true.

$(-2,2)$is the solution.

Step-by-step solution

Step 1. Given information 

The system of equations is

$$\begin{gathered} x-3y=-8 \\ -3x-y=4 \end{gathered}$$

Solution to check are$(2,-2),(-2,2)$

Step 2. Checking solution (a)

Plug $x=2,y=-2$into both equations and check whether left side is same as right side

First equation:

$$\begin{gathered} 2-3(-2)=-8 \\ 2+6=-8 \\ 8=-8 \end{gathered}$$

Left side is not same as right side.

So, $(2,-2)$is not the solution for first equation.

Second equation:

$$\begin{gathered} -3\left(2\right)-(-2)=4 \\ -6+2=4 \\ -4=4 \end{gathered}$$

Left side is not same as right side.

So, $(2,-2)$is not the solution for second equation.

Hence, $(2,-2)$does not make both equations true.

Step 3. Checking solution (b)

Plug $x=-2,y=2$into both equations and check whether the left side is the same as the right side

First equation:

$$\begin{gathered} -2-3\left(2\right)=-8 \\ -2-6=-8 \\ -8=-8 \end{gathered}$$

So, $(-2,2)$is the solution of the first equation.

Second equation:

$$\begin{gathered} -3(-2)-2=4 \\ 6-2=4 \\ 4=4 \end{gathered}$$

So, $(-2,2)$is the solution of the second equation.

Hence,$(-2,2)$is solution of both equations.