Question
What is the graphical representation of the following equations?
3x + 2y = 80 and 4x + 3y = 110
- Intersecting lines
- Parallel lines
- Overlapping lines
- None of the above
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 graphical representation of the equations: 3x + 2y = 80 and 4x + 3y = 110
The correct answer is: Intersecting lines
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.
There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.
When the lines are coinciding with each other then there is infinite number of solutions.
Now we have given the equations as:
Comparing it, we get:
So it shows that the lines are intersecting lines and has 1 solution.
So here we were asked the nature of the equations, so we used the concept of linear equations and understood with an example that when two lines are intersecting with each other, there is 1 solution for these pair of equations.
Related Questions to study
If a linear equation has one variable, what is it called?
Here the concept of Linear equations and Linear equations in two variables were used. There is only one distinct solution for each linear equation with one variable. So the answer is Linear equation in One variable.
If a linear equation has one variable, what is it called?
Here the concept of Linear equations and Linear equations in two variables were used. There is only one distinct solution for each linear equation with one variable. So the answer is Linear equation in One variable.
If a linear equation has two variables, what is it called?
Here the concept of Linear equations and Linear equations in two variables were used. Two or more equations with the same solution make up a system of linear equations. Each equation in a system of linear equations can be represented by a straight line, and the intersection of two or more such lines is the solution.
If a linear equation has two variables, what is it called?
Here the concept of Linear equations and Linear equations in two variables were used. Two or more equations with the same solution make up a system of linear equations. Each equation in a system of linear equations can be represented by a straight line, and the intersection of two or more such lines is the solution.
What is the point of intersection of the line with the coordinate axes?
So here in this question we were asked about the point of intersection of coordinate axis. We used the concept of coordinate system and found out that its origin (0,0). The coordinate system is compared to a grid-based map. Two axes that are parallel to one another are what make up its lines.
What is the point of intersection of the line with the coordinate axes?
So here in this question we were asked about the point of intersection of coordinate axis. We used the concept of coordinate system and found out that its origin (0,0). The coordinate system is compared to a grid-based map. Two axes that are parallel to one another are what make up its lines.
How many solutions does the system of linear equations have?
y = -2x + 4 and 7y = -14x + 28
So here we have given two equations, y = -2x + 4 and 7y = -14x + 28 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 an infinite number of solution.
How many solutions does the system of linear equations have?
y = -2x + 4 and 7y = -14x + 28
So here we have given two equations, y = -2x + 4 and 7y = -14x + 28 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 an infinite number of solution.
How many solutions do the following equations have?
y = -6x + 8 and y = -3x – 4
So here we have given two equations, y = -6x + 8 and y = -3x – 4 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.
How many solutions do the following equations have?
y = -6x + 8 and y = -3x – 4
So here we have given two equations, y = -6x + 8 and y = -3x – 4 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.
How many solutions do the following equations have?
x + y = -2 and 3x + 3y = -6
So here we have given two equations, x + y = -2 and 3x + 3y = -6 and we had to find out how many solutions it have. Using the concept we found out that the system is having coinciding lines and hence it has an infinite number of solutions.
How many solutions do the following equations have?
x + y = -2 and 3x + 3y = -6
So here we have given two equations, x + y = -2 and 3x + 3y = -6 and we had to find out how many solutions it have. Using the concept we found out that the system is having coinciding lines and hence it has an infinite number of solutions.
How many solutions do the following equations have?
y = x + 3 and y = x + 1
So here we have given two equations, y = x + 3 and y = x + 1 and we had to find out how many solutions it have. Using the concept we found out that the system is having parallel lines and hence it has no solution.
How many solutions do the following equations have?
y = x + 3 and y = x + 1
So here we have given two equations, y = x + 3 and y = x + 1 and we had to find out how many solutions it have. Using the concept we found out that the system is having parallel lines and hence it has no solution.
How many solutions do the following equations have?
y = x + 4 and y = –x + 6
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.
How many solutions do the following equations have?
y = x + 4 and y = –x + 6
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.
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.
