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
(detailed description, like an 8th grader wrote it and original)
To solve this system of equations by graphing, we first need to rewrite the second equation in slope-intercept form.
-4x + 4y = 28
4y = 4x + 28
y = x + 7
Now we have the two equations in slope-intercept form:
y = x + 3
y = x + 7
When we graph these two lines on a coordinate plane, we can see that they are parallel lines. This means they will never intersect, so there is no solution to the system of equations.
The graph of the lines will have the same slope (1), but different y-intercepts (3 and 7). This shows us that the lines are parallel and will never meet, indicating that there is no solution that satisfies both equations simultaneously.
i need you to descried an original graph using these equations and solve the system of linear equations by graphing
y = x + 3
-4x + 4y = 28
i need a detailed description, like an 8th grader wrote it and original please.
To graph these two equations, we first need to rewrite the second equation in slope-intercept form.
-4x + 4y = 28
4y = 4x + 28
y = x + 7
Now we can graph the equations on a coordinate plane. The first equation, y = x + 3, has a y-intercept of 3 and a slope of 1 (rise of 1, run of 1). So we start by plotting the point (0, 3) and from there, we go up 1 and to the right 1 to plot another point.
Next, for the second equation, y = x + 7, we start by plotting the y-intercept of 7, which is point (0, 7). From there, we go up 1 and to the right 1 to plot additional points.
When we draw the lines using these points, we can see that they are parallel lines with the same slope but different y-intercepts. This means they will never intersect. Since the lines do not cross, there is no solution that satisfies both equations at the same time.
Therefore, the graph of these equations shows two parallel lines that do not intersect, indicating that there is no solution to the system of linear equations. This visual representation helps us understand that these equations do not have a common solution because they represent parallel lines that run side by side without meeting.