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 solve the system of linear equations by graphing, we will graph each equation individually and find the point of intersection.
First, let's graph the equation y = x + 3. This is a straight line with a y-intercept of 3 and a slope of 1 (since the coefficient of x is 1). We can plot a few points and connect them to draw the line. For example, when x = 0, y = 3. When x = 1, y = 4. When x = 2, y = 5.
Second, let's graph the equation -4x + 4y = 28. To do this, we can rearrange the equation to isolate y: 4y = 4x + 28, which simplifies to y = x + 7. This is another straight line with a y-intercept of 7 and a slope of 1 (since the coefficient of x is 1). We can plot a few points and connect them to draw the line.
Now, we have graphed both equations and we can see that they intersect at the point (2, 5).
The graph shows that the two lines intersect at one point. This means that there is one unique solution to the system of linear equations. The coordinates of the point of intersection, (2, 5), represent the solution to the system.