To graph the equation y = x + 3, we can start by finding a few points that satisfy the equation. We can choose x = 0, x = 1, and x = -1, and find the corresponding y-values.
When x = 0, y = 0 + 3 = 3, giving us the point (0, 3).
When x = 1, y = 1 + 3 = 4, giving us the point (1, 4).
When x = -1, y = -1 + 3 = 2, giving us the point (-1, 2).
Plotting these points and drawing a line through them, we get the graph of y = x + 3, which is a straight line with a positive slope.
To graph the equation -4x + 4y = 28, we can start by isolating y.
Rearranging the equation, we get 4y = 4x + 28, dividing by 4 gives y = x + 7.
Similarly, we can find a few points that satisfy this equation.
When x = 0, y = 0 + 7 = 7, giving us the point (0, 7).
When x = 1, y = 1 + 7 = 8, giving us the point (1, 8).
When x = -1, y = -1 + 7 = 6, giving us the point (-1, 6).
Plotting these points and drawing a line through them, we get the graph of -4x + 4y = 28, which is also a straight line.
When we graph the two equations, we can visually see that the two lines intersect at the point (4, 7). This point represents the solution to the system of linear equations. Thus, the solution to the system of linear equations is x = 4 and y = 7.
The graph of the system of equations y = x + 3 and -4x + 4y = 28 is shown below. The lines intersect at the point (4, 7), which represents the solution to the system.
Graph of the system of linear equations: