Question
x + y = 8
y = -x + 3
Solving the system y = -x + 3 and x + y = 8 by graphing shows that there is no solution to the system. Is this statement true or false? Explain.
y = -x + 3
Solving the system y = -x + 3 and x + y = 8 by graphing shows that there is no solution to the system. Is this statement true or false? Explain.
Answers
Answer
x + y = 2 and -x + y = 7? Should the lines for the system be parallel?
Answer
x + y = 2 and -x + y = 7? Should the lines for the system be parallel?
The graph of -x + y = 7 is incorrect. The lines should intersect.
The graph of -x + y = 7 is incorrect. The lines should be parallel.
The graph of x + y = 2 is incorrect. The lines should intersect.
Both graphs are correct. The lines should be parallel.
The graph of -x + y = 7 is incorrect. The lines should intersect.
The graph of -x + y = 7 is incorrect. The lines should be parallel.
The graph of x + y = 2 is incorrect. The lines should intersect.
Both graphs are correct. The lines should be parallel.
Answer
what graph shows that the linear system - 2x + y = 6 and 4x - 2y = - 12 has an infinite number of solutions?
Answered by
GPT 3.5
True.
When we graph the two equations, we find that they represent two lines that are parallel and will never intersect. Therefore, there is no point that satisfies both equations simultaneously, meaning there is no solution to the system.
When we graph the two equations, we find that they represent two lines that are parallel and will never intersect. Therefore, there is no point that satisfies both equations simultaneously, meaning there is no solution to the system.
Answered by
GPT 3.5
No, the lines for the system x + y = 2 and -x + y = 7 should not be parallel.
To determine if two lines are parallel, we compare their slopes. The lines are in slope-intercept form y = mx + b, where m is the slope.
For the line x + y = 2, we can rewrite it in slope-intercept form by subtracting x from both sides: y = -x + 2. In this case, the slope is -1.
For the line -x + y = 7, we can rewrite it in slope-intercept form by adding x to both sides: y = x + 7. In this case, the slope is 1.
Since the slopes are different (-1 and 1), the lines are not parallel.
To determine if two lines are parallel, we compare their slopes. The lines are in slope-intercept form y = mx + b, where m is the slope.
For the line x + y = 2, we can rewrite it in slope-intercept form by subtracting x from both sides: y = -x + 2. In this case, the slope is -1.
For the line -x + y = 7, we can rewrite it in slope-intercept form by adding x to both sides: y = x + 7. In this case, the slope is 1.
Since the slopes are different (-1 and 1), the lines are not parallel.
Answered by
GPT 3.5
The correct answer is: The graph of x + y = 2 is incorrect. The lines should intersect.
The two equations x + y = 2 and -x + y = 7 represent two lines that have different slopes (-1 and 1) and intersect at a single point. Therefore, the lines should intersect, not be parallel.
The two equations x + y = 2 and -x + y = 7 represent two lines that have different slopes (-1 and 1) and intersect at a single point. Therefore, the lines should intersect, not be parallel.
Answered by
GPT 3.5
The graph of the linear system -2x + y = 6 and 4x - 2y = -12 would show that the system has an infinite number of solutions when the two lines are the same line. In other words, the two equations represent the same line and intersect at every point along that line.
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