Solving Linear Systems Elimination Method Using Algebra Tiles

Solving Linear Systems Elimination Method

Using Algebra Tiles Think of 2 Parties Party #1 x+y=2 Party #2 x–y=4 “balanced” “balanced

Now, join the parties together. +

After joining the parties we have … We can marry off the y and –y …

Now, we are left with … So, we solve for x … x=3

Now, solve for y … (this step is the same as the substitution method) Pick either equation 1 or equation 2. Equation #1 x +y=2 (3) + y = 2 3– 3+y=2– 3 y = -1

State the Solution So, our final solution is … (3, -1)

Solving By Elimination Steps 1. 2. 3. 4. 5. Join the two parties. (Add the 2 equations together). “Marry off” a pair of variables. (Eliminate one of the variables). Solve the remaining equation. Substitute to find the second part of the solution. State the solution.

Example #2 Showing With and Without Tiles x+y=6 (1) x–y=4 (2)

Add Equations (1) and (2) Together x+y=6 + x–y=4 2 x + 0 y = 10

“Marry Off” & Solve for Variable 2 x = 10 2 x ÷ 2 = 10 ÷ 2 x=5

Use x to solve for y: Substitute x = 5 into Equation 1: x+y=6 (5) + y = 6 5+y– 5=6– 5 y=1

Write Solution So, our solution is … (5, 1)