Mathematics
Grade-8
Easy
Question
How many solutions are there when the graphs of linear equations in two variables
intersect at one point?
- One solution
- Two solutions
- Three solutions
- Infinite solutions
Hint:
Find common points that much solution they can have
The correct answer is: One solution
So , if two lines intersect at one point they will have exactly one solution because there is only one point
which can satisfy both the equations .
So , exactly one solution .
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![space 4 space x minus 6 space y equals 15
space space 2 space x minus 3 space y equals 5](data:image/png;base64,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)
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![space 4 space x minus 6 space y equals 15
space space 2 space x minus 3 space y equals 5](data:image/png;base64,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)
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