Solve the following system of linear equations by graphing. Graph on your own piece of paper. In your submitted answer, describe what the graph looks like and what this tells you about the solution to the system of linear equations. y=x+3 −4x+4y=28
To graph the system of linear equations, we first need to rewrite them in slope-intercept form (y = mx + b).
1. y = x + 3
2. -4x + 4y = 28
4y = 4x + 28
y = x + 7
Now, we can graph these two equations on the same coordinate plane.
For the first equation y = x + 3:
- Plot the y-intercept at (0, 3)
- Use the slope of 1 to go up 1 and right 1, and plot another point. Connect the points to draw a line.
For the second equation y = x + 7:
- Plot the y-intercept at (0, 7)
- Use the slope of 1 to go up 1 and right 1, and plot another point. Connect the points to draw a line.
The two lines will intersect at a point (2, 5).
This intersection point represents the solution to the system of linear equations. In this case, the solution is x = 2 and y = 5. This means that the two lines intersect at the point (2, 5), which satisfies both equations simultaneously.
Therefore, the graph shows that the system of linear equations has a unique solution at the point (2, 5).