Question

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

$\begin{array}{c}x+y=6\\ x-y=4\end{array}$

Short answer

The required solution is represented by $\left(5,1\right)$.

Step-by-step solution

Step 1. Make the required graph and determine the intersection point.

Represent the provided equations in the form of graphs.

Graph of the provided equations are meeting at only one point that is $\left(5,1\right)$.

Step 2. Perform the checking.

The obtained solution is 1 in count that is why the provided equation has only one solution. The obtained point is in the form of $\left(x,y\right)$ so perform substitution of the obtained values of x and y into both of the provided equations for checking.

$$\begin{gathered} 5+1\stackrel{?}{=}6 \\ 6=6\text{True} \end{gathered}$$

$\begin{array}{l}5-1\stackrel{?}{=}4\\ 4=4\text{True}\end{array}$

Step 3. Write the conclusion.

As the substitution of obtained solution returns a true statement so it is the required solution.