Solve each system graphically. Be sure to check your solution.

If a system has an infinite number of solutions, use set-builder notation to write the solution set.If a system has no solution, state this. I tried this and found no solution, is this right?

x + y = 9
x - y = 1

x + y = 9

x - y = 1
Sum: 2x + 0 = 10
X = 5

In Eq1, replace x with 5:
5 + y = 9
Y = 4

Solution set: (x,y) = (5,4).

To solve the given system of equations graphically, we need to plot the graphs of both equations on a coordinate plane and find the point where they intersect, if they do intersect at all.

1. Begin by solving each equation for y:
Equation 1: x + y = 9 -> y = 9 - x
Equation 2: x - y = 1 -> y = x - 1

2. Now, we can plot the graphs of the two equations on a coordinate plane. To do this, choose a range of x-values, substitute them into the equations to find the corresponding y-values, and plot the points.

Let's choose a range of x-values from -5 to 5 and substitute them into the equations:

For Equation 1:
When x = -5, y = 9 - (-5) = 14
When x = 0, y = 9 - 0 = 9
When x = 5, y = 9 - 5 = 4

For Equation 2:
When x = -5, y = -5 - 1 = -6
When x = 0, y = 0 - 1 = -1
When x = 5, y = 5 - 1 = 4

Plotting these points on a graph, we can draw the lines representing the equations.

3. Analyze the graph:
By examining the graph, we can observe that the two lines intersect at the point (5, 4). This intersection point represents the solution to the system of equations. Therefore, the solution to the system is x = 5 and y = 4.

Now, let's check our answer by substituting the values of x and y back into the original equations:

For Equation 1: 5 + 4 = 9 (True)
For Equation 2: 5 - 4 = 1 (True)

Both equations hold true when we substitute x = 5 and y = 4, which confirms that (5, 4) is indeed the solution to the system.

In this case, since the system has a unique solution, we do not need to use set-builder notation.