Which ordered pair could possibly be a solution of the graphed system of equations? Why?
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Part 1
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A coordinate system has an unlabeled horizontal x-axis and an unlabeled vertical y-axis. A line that falls from left to right crosses the y-axis above the x-axis. A second line that falls from left to right crosses the x-axis to the right of the y-axis. The second line is steeper than the first line. The point where the two lines intersect is above the x-axis and to the right of the y-axis.
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Part 1
Choose the correct answer below.
A.
The point (−5,−5) is a possible solution because the lines intersect in quadrant III.
B.
The point (5,5) is a possible solution because the lines intersect in quadrant I.
C.
The point (5,−5) is a possible solution because the lines intersect in quadrant IV.
D.
The point (−5,5) is a possible solution because the lines intersect in quadrant II.
The correct answer is D. The point (-5, 5) is a possible solution because the lines intersect in quadrant II.
Based on the given information, we can conclude the following:
- The first line falls from left to right and crosses the y-axis above the x-axis, indicating a positive y-intercept.
- The second line falls from left to right and crosses the x-axis to the right of the y-axis, indicating a positive x-intercept.
- The second line is steeper than the first line.
- The point where the two lines intersect is above the x-axis and to the right of the y-axis.
Now let's analyze the options:
A. The point (-5, -5) is a possible solution because the lines intersect in quadrant III.
This option is incorrect because the lines intersect above the x-axis, not in quadrant III.
B. The point (5, 5) is a possible solution because the lines intersect in quadrant I.
This option is incorrect because the lines intersect above the x-axis, not in quadrant I.
C. The point (5, -5) is a possible solution because the lines intersect in quadrant IV.
This option is also incorrect because the lines intersect above the x-axis, not in quadrant IV.
D. The point (-5, 5) is a possible solution because the lines intersect in quadrant II.
This option is incorrect because the lines intersect above the x-axis, not in quadrant II.
Therefore, there is no correct answer given the information provided.
To determine the possible solutions for the given graphed system of equations, we need to analyze the position of the lines in the coordinate plane.
Based on the description provided, we know:
- The first line falls from left to right and crosses the y-axis above the x-axis.
- The second line falls from left to right and crosses the x-axis to the right of the y-axis.
- The second line is steeper than the first line.
- The point where the two lines intersect is above the x-axis and to the right of the y-axis.
Let's go through the answer choices and evaluate their validity:
A. The point (-5, -5) is a possible solution because the lines intersect in quadrant III.
- In this case, the point (-5, -5) does not match the given description, as it is below the x-axis, not above it.
B. The point (5, 5) is a possible solution because the lines intersect in quadrant I.
- This point matches the given description as it is above the x-axis and to the right of the y-axis. It could be a potential solution.
C. The point (5, -5) is a possible solution because the lines intersect in quadrant IV.
- This point does not match the given description, as it is below the x-axis, not above it.
D. The point (-5, 5) is a possible solution because the lines intersect in quadrant II.
- This point does not match the given description, as it is to the left of the y-axis, not to the right.
Therefore, the correct answer is B. The point (5, 5) is a possible solution because the lines intersect in quadrant I.