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0:18 2:54 Suggested clip Infinitely Many Solutions or No Solution? Equations Special Cases YouTubeStart of suggested client of suggested clip Infinitely Many Solutions or No Solution? Equations Special Cases
0:08 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
A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line). This article reviews all three cases. One solution. A system of linear equations has one solution when the graphs intersect at a point.
When both equations have the same slope, but not the same y-intercept, they'll be parallel to each other and no intersections means no solutions. When both equations have different slopes than regardless of the y-intercept they'll intersect for certain, therefore it has exactly one solution.
2:23 11:01 Suggested clip Determine if a system has one solution, no solution, or infinite YouTubeStart of suggested client of suggested clip Determine if a system has one solution, no solution, or infinite
0:06 5:41 Suggested clip determining the number of solutions to a system of equations without YouTubeStart of suggested client of suggested clip determining the number of solutions to a system of equations without
2:25 7:29 Suggested clip One Solution, No Solution, or Infinitely Many Solutions — Consistent YouTubeStart of suggested client of suggested clip One Solution, No Solution, or Infinitely Many Solutions — Consistent
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.
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