Question

Determine whether the ordered pair is a solution to the system $\left\{\begin{array}{l}x-3y=-8\\ -3x-y=4\end{array}\right.$

1. $(2,-2)$
   
2. $(-2,2)$
   

Short answer

Part (a) The ordered pair $(2,-2)$is not a solution to the system.

Part (b) The ordered pair $(-2,2)$is a solution to the system.

Step-by-step solution

Part (a) Step 1. Given Information.

We are given a system of equations,

$\left\{\begin{array}{l}x-3y=-8\\ -3x-y=4\end{array}\right.$

We need to determine whether the point $(2,-2)$is a solution to the system or not.

Part (a) Step 2. Substitute the ordered pair in the first equation. 

Substitute $2$for $x$and $-2$for $y$in the equation $x-3y=-8$. We get,

$\begin{array}{rcl}2-3\times (-2)& =& -8\\ 2+6& =& -8\\ 8& =& -8\end{array}$

This is a false statement. So, the point $(2,-2)$does not satisfy the first equation.

So, the point $(2,-2)$is not a solution to the given system.

Part (b) Step 1. Given Information.

We are given a system of equations,

$\left\{\begin{array}{l}x-3y=-8\\ -3x-y=4\end{array}\right.$

We need to determine whether the point $(-2,2)$is a solution to the system or not.

Part (b) Step 2. Substitute the ordered pair in the first equation. 

Substitute $-2$for $x$and $2$for $y$in the equation $x-3y=-8$. We get,

localid="1644334956842" $\begin{array}{rcl}-2-3\times 2& =& -8\\ -2-6& =& -8\\ -8& =& -8\end{array}$

This is a true statement, so the point $(-2,2)$satisfy the first equation.

Part b Step 3. Substitute the ordered pair in the second equation 

Substitute $-2$for $x$and $2$for $y$in the equation $-3x-y=4$we get

$\begin{array}{rcl}-3\times (-2)-2& =& 4\\ 6-2& =& 4\\ 4& =& 4\end{array}$

This is a true statement, so the point $(-2,2)$satisfy the second equation.

So the point $(-2,2)$is a solution to the given system.