Transcript PPT - Militant Grammarian

Solving Systems of Equations
Using Elimination
Students will be able to solve systems
of equations using elimination
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.
3x  2y  4

4x  2y  18
Step 1: Find the value of one variable.
3x + 2y = 4
4x – 2y = -18
7x
= -14
x = -2
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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 Substitute -2 in for x.
2y = 10
y=5
Second part of the solution.
The solution is the ordered pair (-2, 5).
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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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Example 2 - Using Elimination
Use elimination to solve the system of equations.
3x  5y  16

2x  3y  9
Step 1: To eliminate x, multiply both sides of
the first equation by 2 and both sides of the
second equation by –3.
2(3x + 5y) = 2(–16)
6x + 10y = –32 Add the
→
–3(2x + 3y) = –3(–9)
–6x – 9y = 27 equations.
First part of the solution: y = –5
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Example 2 (Cont.)
Step 2: Substitute the y-value into one of the
original equations to solve for x.
3x + 5(–5) = –16
3x – 25 = –16
3x = 9
x=3
Second part of the solution
The solution for the system is (3, –5).
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