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). make this like a 8th grader wrote it
So, to graph these two equations, first we write them in y = mx + b form.
So, for the first one y = x + 3, we plot the point (0, 3) and go up 1 and to the right 1 to get another point, and draw a line.
For the second one y = x + 7, we plot the point (0, 7) and go up 1 and to the right 1 to get another point, and draw a line.
The two lines intersect at the point (2, 5), which is the solution to the equations. This means x = 2 and y = 5. So, the system has a solution at (2, 5).