Question

Solve each system by graphing:

$$\begin{gathered} x+y=6 \\ x-y=2 \end{gathered}$$

Short answer

The solution is$(4,2)$

Step-by-step solution

Step 1. Given information 

The system of equations is

$$\begin{gathered} x+y=6 \\ x-y=2 \end{gathered}$$

Step 2. Finding x and y-intercepts of the first equation

The first equation is

$x+y=6$

x-intercept:

Plug $y=0$and find $x$

role="math" localid="1647705545518" $$\begin{gathered} x+0=6 \\ x=6 \end{gathered}$$

So, x-intercept is $(6,0)$

y-intercept:

Plug $x=0$and find $y$

$$\begin{gathered} 0+y=6 \\ y=6 \end{gathered}$$

So, the y-intercept is $(0,6)$

Step 3. Finding x and y-intercepts of the second equation

Second equation is

$x-y=2$

x-intercept:

Plug $y=0$and find $x$

$$\begin{gathered} x-0=2 \\ x=2 \end{gathered}$$

So, the x-intercept is $(2,0)$

y-intercept:

Plug $x=0$and find $y$

$$\begin{gathered} 0-y=2 \\ -y=2 \\ y=-2 \end{gathered}$$

So, the y-intercept is$(0,-2)$

Step 4. Sketch graph of both equations

First equation:

Locate points $(6,0),(0,6)$on the graph and then join them to get the graph

Second equation:

Locate points$(2,0),(0,-2)$ on the graph and then join them to get the graph

So, the graph is

Step 5. Identify the solution of the system

If the lines intersect, identify the point of intersection.

If lines are parallel, the system has no solution.

If lines are same, the system has an infinite number of solutions.

The graph is

Here, the intersection point is$(4,2)$