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 need to rewrite the second equation in slope-intercept form:
−4x + 4y = 28
4y = 4x + 28
y = x + 7
Now we have the two equations to graph:
y = x + 3
y = x + 7
Both equations are in slope-intercept form, so we can easily see that they have different y-intercepts and slopes. The first equation y = x + 3 has a y-intercept of 3 and a slope of 1. The second equation y = x + 7 has a y-intercept of 7 and a slope of 1.
When we graph these two lines, we can see that they are parallel and will never intersect. This means that there is no solution to this system of linear equations because the two lines are parallel and never cross each other.
Therefore, the graph shows two parallel lines that do not intersect, indicating that there is no solution to the system of linear equations.