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two equations, two unknowns - i

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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

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algebra, equations, and inequalities