Solving Linear Systems

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Solving Linear Systems

• Elimination Method

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Using Algebra Tiles

• Think of 2 Parties

Party 1 x y 2 Party 2 x y 4

balanced balanced
3

• Now, join the parties together.

4

• After joining the parties we have

We can marry off the y and y
5

• After joining the parties we have

We can marry off the y and y
6

• After joining the parties we have

We can marry off the y and y
7

• Now, we are left with

So, we solve for x
x 3
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• 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
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State the Solution

• So, our final solution is
• (3, -1)

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Solving By Elimination Steps

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

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Example 2Showing With and Without Tiles
x y 6 ? (1) x y 4 ? (2)
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Add Equations (1) and (2) Together
x y 6 x y 4 2x 0y 10
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Marry Off Solve for Variable
2x 10 2x 2 10 2 x 5 x 5
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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

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Write Solution

• So, our solution is
• (5, 1)