Solve the following system of linear equations by graphing. Graph on your on piece of paper. In your submitted answer, describe what the graph looks like and what this tells you about the situation to the system of linear equations.
y=x + 3
-4x + 4y = 28
To solve this system of linear equations by graphing, we first need to rearrange the second equation to be in slope-intercept form.
-4x + 4y = 28
4y = 4x + 28
y = x + 7
Now we can graph both equations on the same graph. The first equation, y = x + 3, has a y-intercept of 3 and a slope of 1 (rise 1, run 1). The second equation, y = x + 7, also has a y-intercept of 7 and a slope of 1.
Upon graphing these two lines, you should see that they are parallel to each other and will never intersect. This means that there is no solution to this system of linear equations, as the two lines will remain separate and never cross paths. This tells us that the equations are inconsistent and there is no common solution that satisfies both equations simultaneously.