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two equations, two unknowns - i
summary
the essence of solving algebraic equations with two variables lies in understanding that a single equation can have an infinite number of solutions, and these solutions, when plotted on an x-y graph, form a straight line. to find a unique solution for two variables, one must employ a system of equations approach, utilizing either substitution or elimination methods.
- a single equation with two variables typically has an infinite number of solutions, all of which lie on a straight line in an x-y graph.
- a system of equations with two variables generally has a unique solution, representing the point where the lines intersect on a graph.
- the substitution method involves solving one equation for one variable and substituting the result into the other equation to find the unique values of both variables.
- substitution is most effective when one of the variables in any of the equations has a coefficient of plus or minus one, as it avoids the complexity of dealing with fractions.
- the elimination method, to be discussed in the next lesson, is preferred when substitution is not convenient, typically in scenarios where solving for a variable leads to fractions.
chapters
00:01
introduction to equations with two variables
01:37
the concept of infinite solutions
02:55
solving systems of equations: substitution method
06:27
optimizing the substitution method
