Question
How many solutions do the following equations have?
y = x + 4 and y = –x + 6
- No solution
- One solution
- Three solutions
- Infinite solutions
Hint:
When two or more linear equations interact, we have a system of linear equations. There are three systems of equation:
- No solution: System with parallel lines
- One solution: System with intersecting lines
- Infinitely many solutions: System with coinciding lines
Here in this question, we have given two equations where we have to find which system it belongs to and how many solutions it has.
The correct answer is: One solution
The value or values that hold true for each equation in the system constitute the solution to the system of equations. In this question we have given two equations, those are:
We have to find how many solutions It has. Let's first re-arrange the terms, we get:
So these equations have 1 solution.
So here we have given two equations, y = x + 4 and y = –x + 6 and we had to find out how many solutions it have. Using the concept we found out that the system is having intersecting lines and hence it has 1 solution.
Related Questions to study
How many solutions do equations have when they overlap with each other?
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.
How many solutions do equations have when they overlap with each other?
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.
How many solutions that the equations have when they are parallel?
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.
How many solutions that the equations have when they are parallel?
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.
How many solutions that the equations have when they intersect at a point?
So here we were asked how many solutions that the equations have when they intersect at a point, so we used the concept of linear equations and understood that when two lines intersect at a point, there is only one solution.
How many solutions that the equations have when they intersect at a point?
So here we were asked how many solutions that the equations have when they intersect at a point, so we used the concept of linear equations and understood that when two lines intersect at a point, there is only one solution.
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