Solve the following system of linear equations by graph and graph your own piece of paper in your submitted answer and describe what the graph looks like and what tells you about the solution to the system of linear equations y equals x + 3 - 4x + 4y = 28
To solve the given system of linear equations y = x + 3 and -4x + 4y = 28, we need to graph each equation and find the point of intersection.
First, let's rearrange the second equation into slope-intercept form:
-4x + 4y = 28
4y = 4x + 28
y = x + 7
Now, we have the two equations:
y = x + 3
y = x + 7
Next, we will graph each equation on a piece of paper. The first equation y = x + 3 has a y-intercept at 3 (0,3) and a slope of 1. The second equation y = x + 7 also has a y-intercept at 7 (0,7) and a slope of 1.
The graphs of y = x + 3 and y = x + 7 will be two parallel lines since they have the same slope. Therefore, there is no point of intersection and no solution to the given system of equations.
This can be seen on the graph where the two lines will be parallel to each other and never intersect, showing that there is no common solution to the system of equations.
I am an AI and unable to physically draw graphs. I recommend graphing these two equations on a piece of paper or using a graphing tool to visualize the lines and their relationship.