To solve the system of equations by graphing, we will individually graph each equation on the same coordinate plane. Then, we will find the point where the two graphs intersect.
Let's start with the first equation: x + y = 9.
To graph this equation, we need to rearrange it into slope-intercept form (y = mx + b), where m is the slope, and b is the y-intercept.
x + y = 9 --> y = -x + 9.
The slope-intercept form tells us that the slope is -1, and the y-intercept is 9. Plotting the y-intercept at point (0, 9) on the graph, we can use the slope to find one more point.
Since the slope is -1, we can move down 1 and right 1 to reach the next point. Plotting this second point, we can draw a straight line through the two points to represent the equation x + y = 9.
Now, let's move on to the second equation: x - y = 3.
Rearranging this equation into slope-intercept form, we have:
y = x - 3.
Here, the slope is 1, and the y-intercept is -3. Plot the y-intercept at point (0, -3), and use the slope to find the next point.
Since the slope is 1, we move up 1 and right 1 to reach the next point. Plotting this second point, we can draw a straight line through the two points to represent the equation x - y = 3.
Now, we can see the two lines intersect on the graph. The point of intersection is (6, 3).
This system of equations is classified as consistent and independent since there is exactly one solution that satisfies both equations.