Solving Systems of Solving Systems of Equations Using Equations Using

EliminationElimination

Solving Systems of Solving Systems of Equations Using Equations Using

EliminationElimination

Students will be able to solve Students will be able to solve systems of equations using systems of equations using

elimination elimination

FHS Systems of Equations 2

Solving Systems - Elimination

• Another way to solve systems of equations is with the elimination method.

• With elimination, you get rid of (eliminate)one of the variables by adding or subtracting equations.

• The elimination method is sometimes called the addition and subtraction

method.

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Using Elimination - Example 1

Use elimination to solve the system of equations.

4 2 1

2

8

3 4y

x y

x

Step 1: Find the value of one variable.

3x + 2y = 4

4x – 2y = -18

7x = -14

x = -2

The y-terms have opposite coefficients.

Add the equations to eliminate y.

First part of the solution.

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Example 1 (cont.)

Step 2: Substitute the x-value into one of the original equations to solve for y.

3(-2) + 2y = 4

2y = 10

y = 5 Second part of the solution.

The solution is the ordered pair (-2, 5).

Substitute -2 in for x.

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What if Elimination Does Not Work?

• When you cannot eliminate one of the variables by just adding or subtracting the two equations, it is still possible to solve the system.

• Sometimes you can multiply one or both of the equations by some number that would make elimination possible.

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Use elimination to solve the system of equations.

Example 2 - Using Elimination

Step 1: To eliminate x, multiply both sides of the first equation by 2 and both sides of the second equation by –3.

Add the equations.

First part of the solution: y = –5

1

3 9

3 5

2

6

x y

x y

2(3x + 5y) = 2(–16)

–3(2x + 3y) = –3(–9)

6x + 10y = –32

–6x – 9y = 27

→

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Example 2 (Cont.)

Second part of the solution

Step 2: Substitute the y-value into one of the original equations to solve for x.

The solution for the system is (3, –5).

3x + 5(–5) = –16

3x – 25 = –16

3x = 9

x = 3