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This reduction of the equations to one with a single variable x was very easy because the variable y only had to be subtracted from itself. If the y in the original equations each have unequal multipliers, the solution is not so simple. We still have a way to proceed, though. With the multiplication rule, we can “equalize” the equations so that the y in each one does have a common multiplier. This strategy may remind you of the method for finding common denominators that you learned in fraction addition. In the demonstration below, you will see a small counter to the left of each equation which is in the form ax + by = c. The counter will impose the multiplication rule on each equation. As you change the values in the counter, you will see each term in its equation be multiplied by the number you choose.

Substitution

Elementary Algebra





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Visual Math Learning is a free educational web site featuring an interactive on-line tutorial for teaching elementary mathematics and basic arithmetic for grades K-12 at the pre-algebra level. It is an instructional aid for parents, teachers, and educators of primary, elementary, and middle school students, as well as a resource for lesson plans, homework help, and home schooling math lessons. The tutorial includes games, puzzles, interactive diagrams, and computer animated virtual manipulatives that emphasize active learning concepts by visualization.