Chapter 7.2, Problem 31E

To determine

The matching of the system of linear equation with its graph. The system is consistent or inconsistent.

Answer to Problem 31E

Graph $(b)$ ,one solution,consistent.

Explanation of Solution

Given information:

Match the system of linear equations with its graph. Describe the number of solutions and state whether the system is consistent or inconsistent.

  

The system of the equation are:

  $\{\begin{array}{l}2x-5y=0\\ x-y=3\end{array}$

Calculation:

The given equations are $\{\begin{array}{l}2x-5y=0\\ x-y=3\end{array}$ .

To find the matching the system of linear equation with its graph and the system is consistent or inconsistent thenfirstly will multiply the second equation by $2$ :

  $\begin{array}{l}2(x-y=3)\\ 2x-2y=6\end{array}$

Subtract the above equation from the first equation:

  $\begin{array}{l}\underset{\_}{\begin{array}{l}2x-5y=0\\ 2x-2y=6\\ -\text{ + }-\end{array}}\\ -3y=-6\\ y=2\end{array}$

Substitute the value of $y=2$ in the given first equation to find the value of $x$ :

  $\begin{array}{l}2x-5y=0\\ 2x-5\left(2\right)=0\\ 2x-10=0\\ 2x=10\\ x=5\end{array}$

The values of $x$ and $y$ are $5$ and $2$ .The two lines are intersect in one point and the system is consistent.

The lines are intersected at $\left(5,2\right)$ so, the graph $(b)$ is the only one that fits. The correct solution is graph $(b)$ .

Thus,the solutions graph $(b)$ and the system of equation consists one solution and the system is consistent.