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Warmups – solve using substitution
1. y = x + 4
3x – 2y = -7
3.
Solve by graphing:
x+y=3
2x + 2y = -6
2. 4x + y = 0
2y + x = -7
SUBSTITUTION: SPECIAL CASES
x + y = 16
2y = -2x + 2
x = 16 – y
2y = -2(16 – y) + 2
2y = -32 + 2y + 2
2y = -30 + 2y
0 = -30
False
NO SOLUTION
6x – 2y = -4
y = 3x + 2
6x – 2(3x + 2) = -4
6x – 6x – 4 = -4
-4 = -4
True
INFINITELY MANY
8-3 ELIMINATION USING
ADDITION
Objective: To solve systems of
equations using the elimination
method.
EXAMPLE 1
3x – 2y = 4
4x + 2y = 10
3x – 2y = 4
+ 4x + 2y = 10
7x + 0y = 14
7x = 14
x=2
Substitute!
Rows 1-3: Use first equation
Rows 4-5: Use second equation
Answer: (2,1)
TRY WITH AN ALLSTAR
1) -3x + 4y = 12
3x – 6y = 18
(-24,-15)
2) x + y = 8
x–y=4
(6,2)
EXAMPLE 2
x + y = 18
-1(x + 2y = 25)
x + 2y = 25
-x – 2y = -25
Multiply an equation by (-1)
x + y = 18
+ -x – 2y = -25
0x – y = -7
-y = -7
y=7
Answer: (11,7)
Substitute!
x + 7 = 18
x = 11
TOO
1) 13x + 5y = -11
13x + 11y = 7
2) 3x – 5y = -35
2x – 5y = -30
(-2,3)
(-5,4)
REMEMBER . . .
0 = 10
No Solution
0=0
Infinitely Many
TOO for Homework
1) x + y = 7
2) 3x + y = 5
x + y = 11
2x + y = 10
3) 2x – 5y = -6
-2x + 7y = 14
Homework
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Pg. 473 #15-30 Left Column