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With two variables you need two equations. Get them into a common form such as slope intercept. If they are the same, there are infinite solutions, if they have the same slope and different y-intercept, they have no solution, and if the slopes are different, they have one solution.
If they are the same, there are infinite solutions, if they have the same slope and different y-intercept, they have no solution, and if the slopes are different, they have one solution.
If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions. If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.
If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.
1:51 3:10 Suggested clip How to Determine When a System of Equation Has no Solution by YouTubeStart of suggested client of suggested clip How to Determine When a System of Equation Has no Solution by
No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true. Note that we have variables on both sides of the equation.
0:34 3:40 Suggested clip Determining the Number of Solutions for Systems of Equations YouTubeStart of suggested client of suggested clip Determining the Number of Solutions for Systems of Equations
0:23 3:40 Suggested clip Determining the Number of Solutions for Systems of Equations YouTubeStart of suggested client of suggested clip Determining the Number of Solutions for Systems of Equations
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