The Visual / Auditory / Symbolic / Kinesthetic Approach to Algebra

Solve A Systems of Linear Equations by Linear Combination.

Solve Systems by Linear Combination.
1st:Use 4 display areas -- two for each equation.
Let the top areas (the ones furthest from the user) be for the top equation.
Let the bottom areas (the ones closest to the user) be for the bottom equation.
2nd:Represent each equation.
3rd:Move the variables of each equation to the left (or the right) side and the constants of each equation to the other side.
4th:Pick one variable to eliminate first.
Either variable is appropriate, but, choose the variable that is easy to "zero out," to match the positives with an equal number of negatives to make and remove zeros.
Multiply none, or one, or both equations by constant(s)
so that the coefficients of the chosen variable are opposites.
5th:COMBINE (Add or subtract) the two equations together to eliminate this chosen variables placing the new equation in the top or bottom display areas.
Remove the other display areas once the equations have been added/subtracted.
An infinite number of solutions is indicated by a true statement.
No solution is indicated by a false statement.
7th:Pick, COMBINE, solve -- repeat steps 4-6 for the other variable.
7th:SUBSTITUTE, place, this value in either original equation to solve for the other variable.
8th:State the solution and include values for both variables.

      Example 8 is solved using the alternate linear combination method -- use linear combination twice rather than linear combination for the first variable and substitution for the second variable. It is VERY useful when the first variable turns out to be a fraction.

      Four possible tactics are possible. Two involve the x first and the other two involve the y first. Since the x terms are of opposite signs, just multiply the top equation by 2 and combine the equations., Unit 39   © 2008, A. Azzolino