Question

solve the following system of linear equations by graphing graphing 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 equals x + 3 and
"-4x" + 4 y equals 28

Answer 1

Shorter

Answer 2

To solve the system of linear equations graphically, we need to graph the two equations y = x + 3 and -4x + 4y = 28.

First, let's rewrite the second equation in slope-intercept form y = mx + b:
-4x + 4y = 28
4y = 4x + 28
y = x + 7

Now, let's graph the two equations on the same graph:

For the first equation y = x + 3:
- Plot the y-intercept at 3.
- Use the slope of 1 to find another point by going up 1 unit and to the right 1 unit.
- Draw a straight line through these two points.

For the second equation y = x + 7:
- Plot the y-intercept at 7.
- Use the slope of 1 to find another point by going up 1 unit and to the right 1 unit.
- Draw a straight line through these two points.

The graph will show two lines, one with a steeper slope passing through (0,3) and the other with a less steep slope passing through (0,7). These lines will intersect at a point, which is the solution to the system of equations.

By looking at the graph, you can see that the lines intersect at the point (4,7), which is the solution to the system of linear equations y = x + 3 and y = x + 7. This means that the two equations have exactly one solution, and that solution is x = 4 and y = 7.

Answer 3

The two lines intersect at the point (4, 7). This point represents the solution to the system of linear equations y = x + 3 and y = x + 7. Since the lines intersect at a single point, the system has a unique solution, and that solution is x = 4 and y = 7.