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

y=x+3

−4x+4y=28

(2 points)

one sentence and simple

Answer 1

The graph of the two equations is two straight lines that intersect at one point, indicating that the system of equations has one unique solution.

Answer 2

ok now solve simply

Answer 3

The solution to the system of equations is x = -5, y = -2.

Answer 4

step by step solve simply

Answer 5

1. Start by solving the first equation for y:
y = x + 3

2. Substitute this expression for y into the second equation:
-4x + 4(x + 3) = 28
-4x + 4x + 12 = 28
12 = 28
This is not possible.

Since the equations do not intersect, there is no solution to the system.

Answer 6

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

(2 points)
step by step solve simply

Answer 7

Step 1: Solve the first equation for y:
y = x + 3

Step 2: Rearrange the second equation to slope-intercept form (y = mx + b):
-4x + 4y = 28
4y = 4x + 28
y = x + 7

Step 3: Graph both equations on the same set of axes. The first equation has a y-intercept at 3 and a slope of 1, making it a line that passes through (0,3). The second equation also has a y-intercept at 7 but a different slope of 1, so it will be a parallel line that passes through (0,7).

Step 4: The two lines are parallel and do not intersect. This indicates that the system of equations has no solution as there are no values of x and y that satisfy both equations simultaneously.

Therefore, the system of equations is inconsistent.