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)
Math Short Answer Rubric (2 points)
Points Awarded Criteria
2
The answer is correct. The student made no errors while solving.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
1
The answer is partially correct. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Some work is shown or explained.
0 The question is not answered.
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To solve the system of linear equations by graphing, we need to graph the two equations y = x + 3 and -4x + 4y = 28.
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.