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
To graph the system of linear equations y = x + 3 and -4x + 4y = 28, we first need to put the second equation in slope-intercept form.
-4x + 4y = 28
4y = 4x + 28
y = x + 7
Now we have the two equations:
y = x + 3
y = x + 7
When graphing these lines on a piece of paper, we see that both equations are linear and have the same slope of 1 (the coefficient of x). However, their y-intercepts are different – one being 3 and the other being 7.
Because the lines have the same slope but different y-intercepts, they are parallel to each other and will never intersect. This means that there is no solution to this system of linear equations. In other words, there are no values of x and y that satisfy both equations simultaneously.