The Visual / Auditory / Symbolic / Kinesthetic Approach to Algebra

Solve A Systems of Linear Equations by Substitution.

      Example 3a. in the Warm Ups, from the last page and just below, is a SYSTEM of linear equations presented as a SINGLE sophisticated linear equation. To solve it, substitution is employed. Below, examine it now from a linear system perspective.

Solve Linear Systems by Substitution.
1st:Use two display areas side-by-side for representing an equation. (These will later be moved to the top away from the user.)
2nd:Pick one equation to solve for one variable. Take the easy equation and the easy variable or use another method.
3rd:Solve the equation for the variable of choice.
4th:Move the solved equation in the side-by-side display areas to the top, away from the user, and use two additional side-by-side display areas for the other equation, placing them on the bottom close to the user.
5th:Represent the other equation IN THE STORAGE AREAS ABOVE THE DISPLAY AREAS.
6th:In the bottom display areas, SUBSTITUTE, replace, each of the solved variable tiles with the expression found in the third step and duplicate exactly all other tiles.
7th:Solve the equation from the step six.
8th:Move the easy equation to the top storage areas above the display areas.
9th:In the top display areas, SUBSTITUTE, replace, each of the other variable tiles with the new value from step 7 and duplicate exactly all other tiles.
10th:Solve the easy equation.
11th:State the solution and include values for both variables., Unit 38   © 2008, A. Azzolino