Question
A system of two linear equations is represented by the graph below.
6-3534498-1573107578426
Which statement about the solution of the system of equations is true?
A
(0,0)(0,0)(0,0) is the only solution.
B
(3,2)(3,2)(3,2) is the only solution.
C
(0,0)\left(0,0\right)(0,0) and (3,2)\left(3,2\right)(3,2) are both solutions.
D
(0,0)(0,6)\left(0,0\right)\left(0,6\right)(0,0)(0,6)and (3,2)\left(3,2\right)(3,2) are all solutions.
Answers
GPT-4o mini
To determine which statement about the solution of the system of linear equations is true, we need to analyze the options based on the potential intersections of the lines represented by the equations.
1. **Option A:** (0,0) is the only solution.
- This means both lines intersect only at the origin. This could be true if the lines are not parallel and cross only at (0,0).
2. **Option B:** (3,2) is the only solution.
- This means both lines intersect only at the point (3,2). This could be true if the lines are not parallel, intersecting only at this specific point.
3. **Option C:** (0,0) and (3,2) are both solutions.
- This means both points (0,0) and (3,2) lie on both lines. This typically would indicate the two lines coincide over those points, usually only true if they are the same line.
4. **Option D:** (0,0) and (3,2) are all solutions.
- This implies that both points lie on both lines; thus both lines would coincide over those points or be the same line.
To decide which statement is true, we would typically analyze the given graph. However, since we don’t have access to it, let’s summarize the implications:
- If the graph shows a single intersection point, only A or B could be true.
- If the graph shows two intersection points, then C or D could be true, depending on the behavior of the lines.
In a typical scenario without visualization, the most common cases would suggest:
- If the lines are not parallel and intersect at a single point, then either A or B.
- If they are the same line or intersect at multiple common points, then C or D.
Without the graph, the likely scenario is either:
- One distinct intersection = A or B
- Multiple points = C or D.
If you have the graph and can describe the intersection points, that will help in making a definitive choice among the options.
1. **Option A:** (0,0) is the only solution.
- This means both lines intersect only at the origin. This could be true if the lines are not parallel and cross only at (0,0).
2. **Option B:** (3,2) is the only solution.
- This means both lines intersect only at the point (3,2). This could be true if the lines are not parallel, intersecting only at this specific point.
3. **Option C:** (0,0) and (3,2) are both solutions.
- This means both points (0,0) and (3,2) lie on both lines. This typically would indicate the two lines coincide over those points, usually only true if they are the same line.
4. **Option D:** (0,0) and (3,2) are all solutions.
- This implies that both points lie on both lines; thus both lines would coincide over those points or be the same line.
To decide which statement is true, we would typically analyze the given graph. However, since we don’t have access to it, let’s summarize the implications:
- If the graph shows a single intersection point, only A or B could be true.
- If the graph shows two intersection points, then C or D could be true, depending on the behavior of the lines.
In a typical scenario without visualization, the most common cases would suggest:
- If the lines are not parallel and intersect at a single point, then either A or B.
- If they are the same line or intersect at multiple common points, then C or D.
Without the graph, the likely scenario is either:
- One distinct intersection = A or B
- Multiple points = C or D.
If you have the graph and can describe the intersection points, that will help in making a definitive choice among the options.