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Write a system of equations that relates the number of adult and student tickets sold to the number of tickets sold and to the total ticket sales. Solve by elimination to find the number of each type of ticket sold. Solve by elimination. 3x -10y = -25 4x + 40y = 20 7x = 15y = 32 x -3y = 20 x -8y = 18 -16x + 16y = -8 24x + 2y = 52 6x -3y = -36 88x -5y = 39 -8x + 3y = -1 2x + 4y = 8 5x + y = -7 A photo studio offers several different packages. Let w equal the cost of a wallet-sized portrait, and let f equal the cost of an 8 times 10 portrait. Write a system of equations that relates the cost of wallet-sized portraits and 8 times 10 portraits to the cost of the basic and deluxe packages. Find the cost of each type of portrait. Two groups of students order burritos and tacos at a local restaurant. One order of 3 burritos and 4 tacos costs S11.33. The other order of 9 burritos and 5 tacos costs $23.56. Write a system of equations that describes this situation. Solve by elimination to find the cost of a burrito and the cost of a taco. Solve by elimination. 3x + 2y = -9 -10x + 5y = -5 4x + 5y = 15 6x -4y = 11 3x -2y = 10 2x + 3y = -2 -2x + 5y = 20 3x -7y = -26 10x + 8y = 2 8x + 6y = 1 9x + 5y = 34 8x -2y = -2 Solve each system using any method. Tell why you chose the method you used. Y = 2x y = x -1 7x + 8y = 25 9x + 10y = 35 x = 12y -14 3y + 2x = 26 -20x + 7y = 137 4x + 5y = 43 5y = x 2x -3y = 7 y = x + 2 y = -2x + 3

Solution

9) 3x - 10y = -25 -------------------- equation 1

4x + 40y = 20 ---------------------- equation 2

multiplying equation 1 by 4 and adding equation 2 to it

12x - 40y =-100

4x + 40y = 20

-------------------------

16x = - 80

x = -5

plugging x =-5 in eqiation 1

3(-5) -10y = -25

-15 - 10y =-25

-10y = -10

y = 1

solution : x =-5 , y = 1

10) 7x+15y = 32

x - 3y = 20

multiplying equation 2 by 5 and adding equation 1 to it

5x - 15y = 100

7x + 15y = 32

--------------------------

12x = 132

x= 11

plugging x = 11 in equation 2

11 - 3y = 20

-3y = 9

y = -3

solution : x= 11 , y = -3

11) x -8y = 18

-16x + 16y =-8

multiplying equation 1 by 2 and adding equation 2 to it

2x - 16y = 36

-16x +16y = -8

-----------------------

-14x = 28

x = -2

plugging x = -2 in equation 1

x -8y = 18

-2 - 8y = 18

-8y = 20

y = -5/2

solution is : x = -2 , y = -5/2

12) 24x + 2y = 52

6x - 3y = -36

multiplying equation 2 by -4

-24x + 12y = 144

24x + 2y = 52

--------------------------

14y = 196

y = 14

plugging y = 14 in equation 1

24x + 2(14) = 52

24x = 24

x = 1

solution is : x = 1 , y = 14