To solve the given system of linear equations by graphing, we need to graph each equation on a coordinate plane and find the point of intersection. The point of intersection will be the solution to the system.
First, let's graph the equation y = x + 3. To do this, we need to identify two points on the graph. One way to do that is to choose some x-values, plug them into the equation, and find the corresponding y-values.
For example, when x = 0, y = 0 + 3 = 3. So we have the point (0, 3) on the graph.
Similarly, when x = -3, y = -3 + 3 = 0. So we have the point (-3, 0) on the graph.
Now, let's graph the second equation, -4x + 4y = 28. To find two points on this line, we can follow the same process of choosing x-values and calculating the corresponding y-values.
For x = 0, we have -4(0) + 4y = 28, which simplifies to 4y = 28, and y = 7. So we have the point (0, 7) on the graph.
For x = -7, we have -4(-7) + 4y = 28, which simplifies to 28 + 4y = 28, and 4y = 0, giving y = 0. So we have the point (-7, 0) on the graph.
Now, we can plot these points on the graph and draw a straight line passing through them.
After plotting the graph, we can observe that the two lines intersect at the point (-4, -1). This point represents the solution to the system of linear equations.
In summary, when we graph the given system of linear equations, we find that the lines intersect at the point (-4, -1). This tells us that (-4, -1) is the solution to the system of equations.