Question

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

$$\begin{gathered} \left\{\begin{array}{c}2x-y=5\\ 5x+2y=8\end{array}\right. \\ x=2,y=-1;(2,-1) \end{gathered}$$

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:

$\begin{array}{rcl}2x-y& =& 5\\ 5x+2y& =& 8\end{array}$

The given solution is $x=2,y=-1$or $(2,-1)$.

Step 2. Check the solution.

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

Substitute $x=2,y=-1$in the first equation.

$\begin{array}{rcl}2\left(2\right)-(-1)& =& 5\\ 4+1& =& 5\\ 5& =& 5\end{array}$

This statement is true.

Substitute $x=2,y=-1$in the second equation.

$\begin{array}{rcl}5\left(2\right)+2(-1)& =& 8\\ 10-2& =& 8\\ 8& =& 8\end{array}$

This statement is true.

Step 3. Conclusion.

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