Ch 3.5
Elimination (multiplication)
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 each equation so the coefficient of the chosen
variable equals the LCM.
4) Add (or subtract) the two equations to each other to
eliminate a variable.
5) Solve for the remaining variable.
Check Your Answers!
Plug in the x and y solutions into BOTH equations to
verify that they both make TRUE statements.
Review
Find the LCM for the following:
1) 2x, 3x
x 1 = 2x 3x
x 2 = 4x 6x
x 3 = 6x
x 4 = 8x
2) 2y, 8y
x 1 = 2y
x 2 = 4y
x 3 = 6y
x 4 = 8y
LCM (x) = 6
LCM (y) = 8
Example 1
Solve using elimination
2x + 3y = 3
x + 6y = -3
1(2x + 3y = 3)
-2( x + 6y = -3)
2x + 3y = 3
+
-2x - 12y = 6
2x + 3y = 3
2x + 3(-1) = 3
−3 +3
2x = 6
x=3
-9y = 9
-9 -9
y = -1
x = 3, y = -1
Example 2
Solve using elimination
2x + 3y = -4
x – 4y = 9
1(2x + 3y = -4)
-2( x – 4y = 9)
2x + 3y = - 4
+
-2x + 8y = -18
2x + 3y = -4
2x + 3(-2) = -4
+6
−6
2x = 2
x=1
11y = -22
11 11
y = -2
x = 1, y = -2
Example 3
Solve using elimination
-2x + 3y = 5
5x – 2y = 4
5(-2x + 3y = 5)
2( 5x – 2y = 4)
-10x + 15y = 25
+
10x – 4y = 8
-2x + 3y = 5
-2x + 3(3) = 5
− 9 −9
-2x = -4
x=2
11y = 33
11 11
y=3
x = 2, y = 3
Example 4
Solve using elimination
15x + 8y = -27
5x + 2y = -13
1(15x + 8y = -27)
-3( 5x + 2y = -13)
15x + 8y = -27
+
-15x – 6y = 39
15x + 8y = -27
15x + 8(6) = -27
− 48 −48
15x = -75
x = -5
2y = 12
2 2
y=6
x = -5, y = 6
Classwork
1)
2x – 9y = 9
-8x – 3y = 3
2)
-7x – 2y = -11
-8x – 4y = -4
3)
-2x – 4y = -22
-7x – 3y = 0
4)
3x + 3y = 18
5x + 7y = 22
5)
7)
-3x – 20y = -7
-2x – 10y = -8
-4x – 4y = 8
7x + 10y = -29
6)
8)
8x – 4y = -28
-7x + 5y = 26
5x + 8y = -2
-6x + 6y = 18