The graphs for the equation y=x+4 and x-y=1.
1. y = x + 4: This is a linear equation in slope-intercept form, where the slope is 1 and the y-intercept is 4.
2. x - y = 1: This equation can be rewritten as y = x - 1. This is also a linear equation, but in slope-intercept form, the slope is 1 and the y-intercept is -1.
Here's how we can solve the system graphically:
1. Graph the first equation (y = x + 4):
Plot the y-intercept (0, 4) on the coordinate plane.
Since the slope is 1, move up one unit and right one unit. This gives you another point (1, 5).
Connect these two points with a straight line. This is the graph of the first equation.
2. Graph the second equation (y = x - 1):
Do the same steps as above, but use the y-intercept (-1, -1) and the slope 1.
Move up one unit and right one unit from (-1, -1) to reach (0, 0).
Connect these points with a straight line. This is the graph of the second equation.
3. Find the intersection point:
The solution to the system of equations is the point where the two lines intersect.
In this case, the lines intersect at the point (2, 3).
Therefore, the solution to the system of equations is x = 2 and y = 3
Graphically, solving a system of equations means finding the point where the corresponding lines intersect. Each line represents one equation, and the point of intersection satisfies both equations simultaneously.
In this case, both lines have the same slope but different y-intercepts. This means they are parallel but not identical. Therefore, the lines only intersect at one point, which is the solution to the system.