1. 6-4: Elimination using Multiplication

2. 1) Use elimination to solve the system: 5x + y = 9 3x – y = 7
(2, -1)
(-2, 1)
(4, -3)
(5, -2) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

3. 2) Use elimination to solve the system: 2x + 4y = -8 2x + y = 1
(3, -2)
(2, -3)
(1, 3)
(-1, 2) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

4. Warmup Scores 4 Daniel Helper 3 Andrew Duncan Anya Augin Naomi Bervin
Alexander Vendress

5. 6-4: Elimination using Multiplication
The difference of involving multiplication is highlighted below in red
Write the system so like terms with the same or opposite coefficients are aligned
Multiply at least one equation by a constant to get two equations that contain opposite terms
Add or subtract the equations, eliminating one variable. Then solve the equation
Substitute the value from Step 2 into one of the equations and solve for the other variable. Write the solutions in (x, y) order

6. 6-4: Elimination using Multiplication
Example of multiplying one equation
2x + y = 23 3x + 2y = 37
No opposites found, but multiply the top equation by -2 to eliminate the “y”
-4x – 2y = x + 2y = 37
-x = Divide by -1
x = 9
(continued next slide)

7. 6-4: Elimination using Multiplication
Example of multiplying one equation
2x + y = 23 3x + 2y = 37
x = 9
2(9) + y = 23 Substitute x = 9
18 + y = 23 Multiply 2(9)
y = 5 Subtract 18 both sides
(9, 5) is the solution

8. Ex 1: Use elimination to solve the system x + 7y = 12 3x – 5y = 10
(1, 5)
(5, 1)
(5, 5)
(1, 1) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

9. 6-4: Elimination using Multiplication
Multiplying both equations
4x + 3y = 8 3x – 5y = -23
No opposites found, but multiply the top equation by 5 and bottom equation by 3 to eliminate the “y”
20x + 15y = 40 9x – 15y = -69
29x = Divide by 29
x = -1
(continued next slide)

10. 6-4: Elimination using Multiplication
Multiplying both equations
4x + 3y = 8 3x – 5y = -23
x = -1
4(-1) + 3y = 8 Substitute x = 9
-4 + 3y = 8 Multiply 4(-1)
3y = Add 4 both sides
y = 4 Divide both sides by 3
(-1, 4) is the solution

11. Ex 2: Use elimination to solve the system 3x + 2y = 10 2x + 5y = 3
(-4, 1)
(-1, 4)
(4, -1)
(-4, -1) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

12. 6-4: Elimination using Multiplication
Word Problem
A personal airplane traveling with the wind flies 520 miles in 4 hours. On the return trip (against the wind), the airplane takes 5 hours to travel the same distance. Find the speed of the airplane without the wind.
Let x be the speed of the airplane
Let y be the speed of the wind
Distance = rate ● time
520 = 4(x + y)
130 = x + y Multiply each side by 2
520 = 5(x – y)
104 = x – y Multiply each side by 3/2
(continued next slide)

13. 6-4: Elimination using Multiplication
Word Problem
Let x be the speed of the boat
Let y be the speed of the current
130 = x + y 104 = x – y
Have opposites, simply add the equations
234 = 2x Divide by 2
117 = x
The plane is traveling 117 miles/hour

14. A helicopter travels 360 miles with the wind in 3 hours
A helicopter travels 360 miles with the wind in 3 hours. The return trip against the wind takes 4 hours. Find the rate of the helicopter in still air.
103 mph
105 mph
100 mph
17.5 mph 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

15. Warm-up + In-Lesson Scores
Participant 1
Participant 2
Participant 3
Participant 4
Participant 5

16. 6-4: Elimination using Multiplication
Assignment
Page 359 – 360
1 – 23, odds