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Two Equations, Two Unknowns - I

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Summary
The essence of solving systems of equations with two variables lies in understanding that a single equation can have an infinite number of solutions, but a system of two equations typically narrows down to a unique solution. This unique solution represents the point of intersection on a graph where both equations meet.
  • A single equation with two variables can have infinite solutions, which, if plotted, lie on a straight line.
  • A system of equations involves two equations with two variables that must satisfy both equations simultaneously, typically resulting in a unique solution.
  • There are two primary methods to solve a system 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 of the equations for one variable and then substituting that expression into the other equation to find a unique solution.
  • The elimination method, which will be covered in the next lesson, is preferred when substitution is not convenient, especially when dealing with fractions.
Chapters
00:01
Introduction to Systems of Equations
01:37
Understanding Infinite Solutions
02:56
Solving Systems of Equations: Substitution Method
00:00
Practical Application of Substitution

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Algebra, Equations, and Inequalities