# Lcm Worksheets

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```					Algebra 2

Lesson 3-2
Solving Systems of Equations
Algebraically (Elimination Method)
What You'll Learn
Why It's Important
 To solve systems of equations by using the
subtraction
 To solve systems of equations by using the
elimination method with multiplication and
 You can use systems of equations to solve
problems involving literature and population
growth
How do I eliminate?
 The elimination method means you add or
subtract the two equations to drop out one of
the variables
 You always look for the variable that is
multiplied by the same number
   If the variables you want to eliminate have the
same coefficient you subtract
   If the variables you want to eliminate have
 Also always make sure you line up the like
terms
Example 1
Use elimination to solve the system of equations

3x - 2y = 4                       The y's should be
eliminated because
they are multiplied

4x + 2y = 10                         by the same
number

Because the 2's are
opposites, then you
equations together
Use elimination to solve the system of
equations
3x - 2y = 4
Now you have to

+ 4x + 2y = 10         substitute x back
into either one of
the two original
equations to figure
7x      = 14            out what y is.

x=2
Use elimination to solve the system of
equations

3x - 2y = 4                3(2) – 2y = 4

4x + 2y = 10                 6 – 2y = 4

x=2                          -2y = -2
y=1
(2,1)
Example 2
 The sum of two numbers is 18. The sum of
the greater number and twice the smaller
number is 25. Find the numbers.
Example 2
 The sum of two numbers is 18. The sum of
the greater number and twice the smaller
number is 25. Find the numbers.
 Let x = the smaller number
 Let y = greater number

x + y = 18
Notice the like
y + 2x = 25            terms are not
lined up
Example 2

y + x = 18                 The y's are both
multiplied by the
y + 2x = 25              same number (1) so
we want to
eliminate the y

This time the
coefficients are
the same so we
subtract the two
equations
Basically to subtract you switch the signs on

  y + x = 18 y + x = 18
-(y + 2x = 25) -y -2x = -25
Substitute 7 for x
in either of the
-1x = -7
two original
equations
x=7
y + 7 = 18
y = 11
(7,11)
What is required to use
elimination?
 To use the method of elimination you have to have
the coefficients of one of the two variables be
identical (or opposites)
 In order to accomplish this you multiply one or both of
the equations by a number that will result in the same
coefficients
Example 3
Use elimination to solve the system of equations
 2x + 3y = 5
 5x + 4y = 16
 I want to eliminate the x's what do I have to
multiply each equation by?
Example 3
Use elimination to solve the system of equations
 5[2x + 3y = 5] 10x +15y = 25
 2[5x + 4y = 16] 10x + 8y = 32
 Do I add or subtract the resulting equations?
Example 3
Use elimination to solve the system of equations
 10x +15y = 25
 -10x - 8y = -32
         7y = -7           2x + 3(-1) = 5
          y = -1
   Original Equations:        2x – 3 = 5
   2x + 3y = 5
2x = 8
   5x + 4y = 16
x=4
(4,-1)
Example 3
Use elimination to solve the system of equations
 2x + 3y = 5
 5x + 4y = 16
 I want to eliminate the y's what do I have to
multiply each equation by?
Example 3
Use elimination to solve the system of equations
 4[2x + 3y = 5]  8x + 12y = 20
 3[5x + 4y = 16] 15x + 12y = 48
 Do I add or subtract the resulting equations?
Example 3
Use elimination to solve the system of equations
 8x + 12y = 20
 -15x - 12y = -48             2(4) + 3y = 5
 -7x         = -28
          x=4                     8 + 3y = 5
   Original Equations:
   2x + 3y = 5
3y = -3
   5x + 4y = 16                       y = -1

(4,-1)
Example 4
 Solve the system of equations by using
elimination.
 x + 3y = 8
 ⅓x + y = 9
Example 4
 Solve the system of equations by using
elimination.
 x + 3y = 8
 ⅓x + y = 9  Multiply by the LCM of the denominators to get rid of the fraction
 3(⅓x + y) = 3(9)  x + 3y = 27

 Now solve this system
 x + 3y = 8
 x + 3y = 27
Example 4
 Solve the system of equations by using
elimination.
 x + 3y = 8
 -(x + 3y = 27)
 0 + 0 = -19
      0 = -19 false
 No Solution

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