Download Objective - To solve a system of linear equations using linear

Ch 5.4 (part 2)
Elimination Method
(multiplying both equations)
Objective:
To solve a system of linear
equations using multi-step elimination
(multiplication and addition).
Rules
1) Rearrange the equations so that “like” terms are lined up.
2) Find the LCM (least common multiple) of the coefficients
pertaining to one of the variables.
3) Multiply one equation so the coefficient of the chosen variable
equals the LCM
4) Multiply one equation so the coefficient of the chosen variable
equals the opposite of the LCM.
5) Add the two equations to each other to eliminate a variable.
6) Solve for the remaining variable.
7) Plug in the solution from step 6 into either equation and solve for
the other variable.
Check Your Answers!
Plug in the x and y solutions into BOTH equations to
verify that they both make TRUE statements.
Example 1
Solve using elimination
3 (2x − 4y = 8)
-2 (3x + 5y = 1)
2x − 4y = 8
2x − 4(-1) = 8
− 4 −4
2x = 4
x=2
6x − 12y = 24
+-6x − 10y = -2
-22y = 22
-22 -22
y = -1
x = 2, y = -1
Example 2
Solve using elimination
5 (-2x + 3y = 5 )
2 ( 5x − 2y = 4)
-2x + 3y = 5
-2x + 3(3) = 5
-9
-9
-2x = -4
x=2
-10x + 15y = 25
+ 10x − 4y = 8
11y = 33
11
11
y=3
x = 2, y = 3
Example 3
Solve using elimination
3 (-7x + 8y = -9 )
7 ( 3x − 5y = -4 )
-7x + 8y = -9
-7x + 8(5) = -9
- 40 -40
-7x = -49
x=7
-21x + 24y = -27
+ 21x − 35y = -28
-11y = -55
-11
-11
y=5
x = 7, y = 5
Classwork
1)
3)
5x + 2y = 4
-8x + 3y = 6
-7x + 8y = -9
3x – 5y = -4
2)
9x + 5y = 10
2x + 2y = -4
4) −3x − 6y = −12
7x − 12y = −24
5)
-3x – 20y = -7
-2x – 10y = -8
6)
-9x – 8y = 1
8x + 10y = 2
7)
-7x – 9y = -7
-4x + 7y = -4
8)
8x + 2y = 10
6x + 5y = -3