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 can rewrite the second equation in slope-intercept form:
-4x + 4y = 28
4y = 4x + 28
y = x + 7
Now we have both equations in the form y = mx + b, where m is the slope and b is the y-intercept.
For the first equation, y = x + 3, the y-intercept is 3, so we plot a point at (0,3) and the slope is 1 (1/1), so we go up 1 and right 1 to plot another point.
For the second equation, y = x + 7, the y-intercept is 7, so we plot a point at (0,7) and the slope is 1 (1/1), so we go up 1 and right 1 to plot another point.
After plotting both lines, they intersect at the point (4,7). This point represents the solution to the system of linear equations y = x + 3 and y = x + 7.
The graph shows that the two lines are parallel, meaning they have the same slope but different y-intercepts. Since parallel lines never intersect, this system of linear equations has no solution.