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do systems of equations with different slopes and different y intercepts have more than one solution

by Ima Farrell DDS Published 3 years ago Updated 2 years ago

That means two equations have different slopes and different y-intercepts. Anytime lines have different slopes they create intersecting lines. A system with intersecting lines is considered consistent because it has at least one solution, and independent because it has exactly one solution.

Full Answer

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.

Can two linear equations have the same slope and same y intercept?

A consistent system is considered to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide so the equations represent the same line. Similarly one may ask, can two different linear functions have the same Y intercept?

What is the difference between parallel lines and different slope intercepts?

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).

What happens when two lines with different slopes have different slopes?

Anytime lines have different slopes they create intersecting lines. A system with intersecting lines is considered consistent because it has at least one solution, and independent because it has exactly one solution. Secondly, when graphing systems of the two slopes are the same?

How many solutions does a system have if the slopes are different?

If the slopes are different, then the lines intersect at one point, which means one solution. In this case, the slopes are -1/2 and -4. Therefore there is one solution.Jan 28, 2015

Can systems of equations have more than one solution?

There can be more than one solution to a system of equations. A system of linear equations will have one point of intersection, or one solution. To graph a system of equations that are written in standard form, you must rewrite the equations in slope -intercept form.

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.Sep 27, 2017

When two lines with different slopes and different y-intercepts Cross how many solutions are there?

If the two lines have different slopes, the system has exactly one solution (whether the lines have the same intercept or different intercepts).

How many solutions does the system of equations above have?

The system of equations above has how many solutions? One approach is to begin solving the system (using the elimination method) and see what happens. As we can see, this equation has infinitely many solutions.

Which systems of equations have infinite solutions?

Which systems of equations have infinite solutions? An independent system of equations has exactly one solution (x,y) . An inconsistent system has no solution, and a dependent system has an infinite number of solutions.Dec 7, 2021

Which is the graph of two lines with different slopes and same or different y-intercept?

If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.

What do you call systems of linear equation with slopes that are different and different y-intercepts?

Parallel Lines: If the two linear equations have the same slope (and different y-intercepts), the lines will be parallel.

What do dependent and inconsistent systems have in common?

If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent .

When two equations have the same slope but different y-intercepts how many solutions exist?

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. There are no points common to both lines; hence, there is no solution to the system.

What is the relationship between the slope and y-intercept to the system of linear equation?

The slope and y-intercept values indicate characteristics of the relationship between the two variables x and y. The slope indicates the rate of change in y per unit change in x. The y-intercept indicates the y-value when the x-value is 0.

When two lines have different slopes the graphs of the equations are?

Step-by-step explanation: When two lines have different slopes, the graphs of the equations are intersecting lines.Oct 20, 2020

What is the system of equations that 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. Click to see full answer.

What is the solution of a system in two variables?

In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common. So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system.

Why are intersecting lines consistent?

Anytime lines have different slopes they create intersecting lines. A system with intersecting lines is considered consistent because it has at least one solution, and independent because it has exactly one solution. Additionally, when graphing systems ...

Is a consistent system dependent?

A consistent system is considered to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide so the equations represent the same line.

Answer

A system of two linear equations is represented graphically as straight lines.

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I believe this is false because if they have different y-intercepts and slopes, there is one solution!!

Answer

A system of linear equations with the same slope and the same y-intercept has infinite solutions (identical lines)

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