solve the following system of linear equations by graphing .in your submitted anser,decribe what the graph looks like and what this tells you about the solution of the system of linear equations
y=x+3
-4x+4y=28
To solve the system of linear equations y=x+3 and -4x+4y=28 by graphing, we first need to rewrite the second equation in slope-intercept form.
-4x + 4y = 28
4y = 4x +28
y = x + 7
Now we can graph both equations on the same coordinate plane:
For the equation y = x + 3:
- Plot the y-intercept at (0,3)
- Use the slope of 1 (rise of 1, run of 1) to find two more points and connect them to draw a line.
For the equation y = x + 7:
- Plot the y-intercept at (0,7)
- Use the slope of 1 (rise of 1, run of 1) to find two more points and connect them to draw a line.
The two lines will intersect at the point (4, 7) on the graph. This intersection point is the solution to the system of linear equations.
The graph of the system of equations will show two lines intersecting at a single point. This tells us that the system has a unique solution.