Question

Graph each system and determine the number of solutions that it has. If it has one solution, name it.

$\begin{array}{l}x-y=1\\ x+y=5\end{array}$

Short answer

The graph of the system is

The number of solutions is 1 and name of the solution is $\left(3,2\right)$.

Step-by-step solution

Step 1. Graph the system of equations.

The given system of equation is:

$x-y=1$ … (1)

$x+y=5$ … (2)

The graph of two equations is drawn as below.

Step 2. Determine the number of solutions.

From the graph it can be observed that the two lines intersect at exactly one point. This intersection point of two lines is nothing but the solution set of given system of equation. Therefore, number of solutions of the set of equations if 1.

Step 3. Name the solutions, if possible.

Now the intersection point of two straight lines shown by eq. (1) and (2) is $\left(3,2\right)$. Therefore, one solution of given system of equation is labelled as $\left(3,2\right)$.