Question

Verify that the values of the variables listed are solutions of the system of equations.

$$\begin{gathered} \left\{\begin{array}{c}3x+2y=2\\ x-7y=-30\end{array}\right. \\ x=-2,y=4;(-2,4) \end{gathered}$$

Short answer

The given values are the solutions because both equations are true for the given values.

Step-by-step solution

Step 1. Given information.

The given equations are:

$\begin{array}{rcl}3x+2y& =& 2\\ x-7y& =& -30\end{array}$

The given solution is $x=-2,y=4$or $(-2,4)$.

Step 2. Check the solution.

If both equations are true for the given values, then the values represent the solution.

Substitute $x=-2,y=4$in the first equation.

$\begin{array}{rcl}3(-2)+2\left(4\right)& =& 2\\ -6+8& =& 2\\ 2& =& 2\end{array}$

This statement is true.

Substitute $x=-2,y=4$in the second equation.

$\begin{array}{rcl}(-2)-7\left(4\right)& =& -30\\ -2-28& =& -30\\ -30& =& -30\end{array}$

This statement is true.

Step 3. Conclusion.

The given values are the solutions because both equations are true for the given values.