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.

Question

short it DO NOT MAKE IT LONG
y=x+3


−4x+4y=28

Answer 1

To solve the system of equations by graphing:

1. First equation: \(y = x + 3\)

   • This is a straight line with a y-intercept of 3 and a slope of 1.

2. Second equation: \(-4x + 4y = 28\)

   • Rearranging this gives \(y = x + 7\) (dividing the entire equation by 4).
   • This line has a y-intercept of 7 and a slope of 1.

Graphing the lines:

• The first line crosses the y-axis at 3 and rises to the right (slope of 1).
• The second line crosses the y-axis at 7 and also rises with the same slope.

Analysis of the graph:

• The lines are parallel because they have the same slope (1) but different y-intercepts (3 and 7).
• Since the lines do not intersect, there is no solution to the system of equations; it is inconsistent.