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
write it how a student would
To solve the system of equations y = x + 3 and -4x + 4y = 28 by graphing, first plot the line y = x + 3. This is a straight line that passes through the y-intercept of 3 and has a slope of 1 (since the coefficient of x is 1). Next, plot the line -4x + 4y = 28, or y = x + 7. This line has a y-intercept of 7 and a slope of 1.
When you graph these two lines, you will see that they intersect at the point (4, 7). This point of intersection is the solution to the system of linear equations, meaning that x = 4 and y = 7.
Describing the graph, both lines intersect at the point (4, 7). This tells us that the system of equations has a unique solution, as there is only one point of intersection between the two lines.