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Two Equations, Two Unknowns - I

Mike McGarry
Lesson by Mike McGarry
Magoosh Expert
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Algebra, Equations, and Inequalities
Summary
Understanding and solving systems of equations with two variables are fundamental skills in algebra, offering a basis for more complex mathematical concepts.
  • A single equation with two variables typically has an infinite number of solutions, which, when plotted on an x-y graph, lie on a straight line.
  • A system of equations involves two equations with two variables that must be satisfied simultaneously, usually resulting in a unique solution where the lines intersect.
  • There are two primary methods for solving systems of equations: substitution and elimination, with substitution being ideal when one of the variables has a coefficient of plus or minus 1.
  • The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to solve for the second variable.
  • Elimination method, which will be covered in the next lesson, is preferred when substitution is not convenient, typically due to the presence of fractions.
Chapters
00:00
Introduction to Systems of Equations
02:56
Solving Systems of Equations: The Big Ideas
03:48
Substitution Method Explained