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