If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:2:12

How many solutions does a system of linear equations have if there are at least two?

Video transcript

you are solving a system of two linear equations in two variables you have found more than one solution that satisfies the system which of the following statements is true but so before even reading these statements let's just think about what's going on so let me draw my axes here let's draw my axes so this is going to be my vertical axis that could be one of the variables and then this is my horizontal variable my horizontal axis that's one of the other variables and maybe for a stake of convention this could be X and this could be Y but they're whatever our two variables are so it's a system of two linear equations so if we're graphing them each of the linear equations in two variables can be represented by a line now there's only three scenarios here one scenario is where the lines don't intersect at all so the only way that you're going to have two lines in two dimensions that don't intersect is if they have the same slope and they have different y-intercepts so that's one scenario but that's not the scenario that's being described here they say you have found more than one solution that satisfies the system here there are no solutions so that's not the scenario that we're talking about there's another scenario where they intersect in exactly one place so they intersect in exactly one place there's one point one X y coordinate right over there that satisfies both of these constraints but this also is not the scenario they're talking about there's there's they're telling us that you have found more than one solution that satisfies the system so this isn't the scenario either so the only other scenario that we can have we don't have parallel lines that don't intersect we don't have lines that only intersect in one place the only other scenario is that we're dealing with the situation where both linear equations are essentially the same constraint they both are essentially representing the same XY relationship that's the only way that I can have two lines and this is only this only applies to linear relationship and lines but the only way that two lines can intersect more than one place more than one place is if they intersect everywhere so in this situation we know that we must have an infinite number of solutions so which of these choices say that this one right here there are infinitely many more solutions to the system right over there