1. Warmups – solve using substitution
y = x x + y = 0
3x – 2y = y + x = -7
Solve by graphing:
x + y = 3
2x + 2y = -6

2. Substitution: Special Cases
x + y = x = 16 – y
2y = -2x + 2
2y = -2(16 – y) + 2
2y = y + 2
2y = y
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

3. 8-3 Elimination Using Addition
Objective: To solve systems of equations using the elimination method.

4. Example 1
3x – 2y = 4 4x + 2y = x + 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)

5. Try with an allstar
1) -3x + 4y = 12 2) x + y = 8 3x – 6y = 18 x – y = 4 (-24,-15) (6,2)

6. Example 2
x + y = 18 x + 2y = 25 Multiply an equation by (-1) x + y = x – 2y = -25 0x – y = -7 -y = -7 y = 7 Substitute! x + 7 = 18 x = 11
-1(x + 2y = 25)
-x – 2y = -25
Answer: (11,7)

7. TOO
1) 13x + 5y = -11 2) 3x – 5y = x + 11y = 7 2x – 5y = -30 (-2,3) (-5,4)

8. Remember . . . 0 = 10 0 = 0 No Solution Infinitely Many
0 = = 0
No Solution Infinitely Many
TOO for Homework
x + y = 7 2) 3x + y = 5 3) 2x – 5y = -6
x + y = x + y = x + 7y = 14

9. Homework
Pg. 473 #15-30 Left Column