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 these two equations, we first need to put them in slope-intercept form (y=mx+b).
The first equation is already in slope-intercept form: y=x+3. This equation has a y-intercept of 3 and a slope of 1. This means we can start plotting the first line by plotting the point (0,3) and using the slope to find more points.
For the second equation, we need to solve for y:
−4x + 4y = 28
4y = 4x + 28
y = x + 7
So the second equation is y=x+7. This equation has a y-intercept of 7 and a slope of 1. We can start plotting this line by plotting the point (0,7) and using the slope to find more points.
When we graph these two lines, we can see that they intersect at the point (4, 7). This means that the solution to the system of linear equations is x=4, y=7.
The graph shows that these two lines intersect at a single point, indicating that there is one unique solution to the system of equations.