Q. 12 - Precalculus Enhanced with Graphing Utilities

Question

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

$$\begin{gathered} \left\{\begin{array}{c}x-y=3\\ -3x+y=1\end{array}\right. \\ x=-2, y=-5;\left(-2,-5\right) \end{gathered}$$

Step-by-Step Solution

Answer

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

Step 1. Given information.

The given equations are:

$\begin{array}{rcl}x-y& =& 3\\ -3x+y& =& 1\end{array}$

The given solution is $x=-2, y=-5$ or $\left(-2,-5\right)$.

Step 2. Check the solution.

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

Substitute $x=-2, y=-5$ in the first equation.

$\begin{array}{rcl}-2-(-5)& =& 3\\ 3& =& 3\end{array}$

This statement is true.

Substitute $x=-2, y=-5$ in the second equation.

$\begin{array}{rcl}-3(-2)+(-5)& =& 1\\ 6-5& =& 1\\ 1& =& 1\end{array}$

This statement is true.

Step 3. Conclusion.

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