Mathematics
Grade-8
Easy
Question
How many solutions do equations have when they overlap with each other?
- No solution
- Two solutions
- Three solutions
- Infinite solutions
Hint:
There are countless possible answers for a system of linear equations. The number that makes every equation in a system of linear equations true is the system's solution. The answers to the two variables in the two equations will be these points' coordinates.
In this question we have asked the number of solutions do equations have when they overlap with each other.
The correct answer is: Infinite solutions
The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.
For example: x=y and x+2y=6
This equation has only one solution as the both the lines intersects at 2,2.
There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.
For example: 2y - 4x =10 and y = 2x + 27
When the lines are coinciding with each other then there is infinite number of solutions.
So the correct option for a number of solutions that the equations have when they are coinciding is infinite.
So here we were asked how many solutions the equations have when they are coinciding, so we used the concept of linear equations and understood with an example that when two lines are coinciding with each other, there are infinite number of solutions.
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So here we were asked how many solutions that the equations have when they are parallel, so we used the concept of linear equations and understood with an example that when two lines are parallel, there is no solution.
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