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Solving a Linear System in Three Variables with no or Infinite Solutions  Problem 3
Alissa Fong
Alissa Fong
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
There are special cases for any system of equations where you have either no solution (meaning, the lines do not intersect at only one point,) or infinite solutions, meaning the lines intersect in some kind of line where there are infinite sets of numbers that would be solutions. (Note with infinite solutions, not any random point will be a solution, but only the infinite set of points that lies on the solution line.) Algebraically, if your variables cancel out and you are left with a true equality statement like 0 = 0, then there are infinite solutions. If your variables cancel out and you are left with a false equality statement, like 0 = 2, then there is no solution to that particular system (often because there are parallel lines.)
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Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
Your tutorials are good and you have a personality as well. I hope you have more advanced college level stuff, because I like the way you teach.”
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Sample Problems (3)
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Solving a Linear System in Three Variables with no or Infinite Solutions
Problem 1 4,216 viewsSolve:
2a − 4b + 6c = 5a + 3b − 2x = 1a − 2b + 3c = 1 
Solving a Linear System in Three Variables with no or Infinite Solutions
Problem 2 3,171 viewsSolve:
3x − 12y + 15z = 9x − 4y + 5z = 32x + 8y − 10z = 6 
Solving a Linear System in Three Variables with no or Infinite Solutions
Problem 3 485 views
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