Solving Linear Systems

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Presentation transcript:

Solving Linear Systems Elimination Method

Using Algebra Tiles Think of 2 Parties Party #1 x + y = 2 Party #2 “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

Pick either equation 1 or equation 2. 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 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 2x + 0y = 10

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

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

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