Can a system of equations with different slopes have more than one solution?
This means that the equations represents the same line and there are infinite number of solution. Therefore, based on the explained above, the conclusion is: Systems of equations with different slopes and different y-intercepts never have more than one solution.
What is the difference between same slope and same intercept?
Same slope, same intercept - Same line, infinite solutions. Same slope, different intercept - Parallel lines, no solution. Different slope, same intercept - One solution (at the intercept). Different slope, different intercepts - One solution (not at the intercept).
When the system of equations has no solution?
No solution: When the lines have the same slope but different y-intercept. This means that the lines are parallel and never intersect, therefore, the system of equations has no solution.
How many solutions can a system of linear equations have?
The systems of linear equations can have: 1. No solution: When the lines have the same slope but different y-intercept. This means that the lines are parallel and never intersect, therefore, the system of equations has no solution. 2. One solution: When the lines have different slopes and intersect at one point in the plane.
Can systems of equations with different slopes and different y-intercepts have one solution?
These two equations have different slopes and different y-intercepts. These are intersecting lines. This system is a consistent system because it has at least one solution and it is independent system because it has exactly one solution.
How many solutions if the slope is different?
ONE UNIQUE SOLUTIONIf the slopes are different, there will be ONE UNIQUE SOLUTION.
How many solutions do two lines in a system have with different slopes have?
If the lines of a system of equations have different slopes; the 2 lines will intersect at only one point and that point will be the solution of the given system of equations. Therefore only one solution will exist for the given system of equations with different slopes.
What happens when two equations have different slopes but the same y-intercept?
Explanation: If two lines have different slopes, they cannot be the same line. However, if they share a y-intercept, that means they cross the y -axis at the same y value. Since the x value is constant on the y-axis (0), they also share an x-value here.
How do you know if a system of equations has one solution?
A system of linear equations has one solution when the graphs intersect at a point.
Are slopes the same in one solution?
A system of linear equations has 1 solution if the lines have different slopes regardless of the values of their y-intercepts. For example, the following systems of linear equations will have one solution. We show the slopes for each system with blue. Notice how the slopes are different.
Can two equations have more than one solution?
Number of Solutions Most linear systems you will encounter will have exactly one solution. However, it is possible that there are no solutions, or infinitely many. (It is not possible that there are exactly two solutions.)
How do you know if a system of equations has two solutions?
If two lines are parallel (and non-coincident) then they do not intersect and there is no solution. If two lines are coplanar and non-parallel, then they will intersect in exactly one point. That is exactly one solution. If they are not coplanar, they will have no intersection and therefore no solution.
When two equations have the same slope but different y-intercepts how many solutions exist?
2 Answers By Expert Tutors You get no solutions if two lines have the same slope and different y-intercepts (y = 2x+1 and y = 2x -3).
How do you tell if a system of equations has no solution or infinitely many?
A linear system has many (infinite) solutions when the two lines are the same (such as y=x+3 and 2y=2x+6 ). And a linear system has no solution when the lines never intersect (in other words, they're parallel; their slopes are equal).
How many solutions are there for a system of linear equations in two variables whose slopes are equal with different y-intercepts?
Thus, there are an infinite number of solutions. Another type of system of linear equations is an inconsistent system, which is one in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts.
Which system of inequalities has no solution?
When two inequalities have parallel lines and the shaded areas do not overlap (i.e., the opposite areas are shaded), then the system has no solution. This means that there is no coordinate point that makes both inequalities true.
How many solutions are there for a system of linear equations in two variables whose slopes are equal with different y-intercepts?
Thus, there are an infinite number of solutions. Another type of system of linear equations is an inconsistent system, which is one in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts.
How many solutions does a linear equation in two variables have if the slopes of the lines are equal but the y-intercepts are not equal?
Therefore, the system of equations has exactly one solution. If the two lines have the same slope but different y-intercepts, then they are parallel lines, and they will never intersect.
What qualifies as no solution?
The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.
How do you tell if a system of equations has no solution or infinitely many?
A linear system has many (infinite) solutions when the two lines are the same (such as y=x+3 and 2y=2x+6 ). And a linear system has no solution when the lines never intersect (in other words, they're parallel; their slopes are equal).
What does it mean when lines have the same slope but different y intercept?
1. No solution: When the lines have the same slope but different y-intercept. This means that the lines are parallel and never intersect, therefore, the system of equations has no solution .
How wide is a rectangular board?
A rectangular board is 1400 millimeters long and 900 millimeters wide. What is the area of the board in square meters? Do not round your answer. =__M
Can a system of equations with different slopes and different y intercepts have more than one solution?
Therefore, based on the explained above, the conclusion is: Systems of equations with different slopes and different y-intercepts never have more than one solution .
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