Substitution Elimination

For questions 9 & 10: One group of friends purchased 10 hot dogs and 5 soft drinks at a cost of $12.50. A second group bought 7 hot dogs and 4 soft drinks at a cost of $9.00. Let x = cost of a hot dog Let y = cost of a soft drink Write a system of linear equations.

One group of friends purchased 10 hot dogs and 5 soft drinks at a cost of $12.50. A second group bought 7 hot dogs and 4 soft drinks at a cost of $9.00.

Let x = cost of a hot dog

Let y = cost of a soft drink

What is the cost of a single hot dog?

• $0.50

• $1.00

• $1.50

• $0.75

The school that Nick goes to is selling tickets to their annual talent show. On the first day of ticket sales, they sold 12 adult tickets and 15 children tickets and made $132. On the second day of ticket sales, they sold 8 adult tickets and 11 children tickets for $92. Let x = cost of an adult ticket Let y = cost of a child ticket Write a system of linear equations.

Solve using substitution or elimination. −4x − 2y = −12 4x + 8y = −24

• (5,-5)

• (6,-6)

• No solution

• Infinitely many solutions

Solve the following system of equations: 5x - 4y = 3 and 2x + 3y = 8

• x = 4, y = 3

• x = 2, y = 1

• x = 3, y = 2

• x = 1, y = 5

29x+37y=103 and 37x+29y = 95 then

• x=1, y=2

• x=2, y=1

• x=3, y=2

• x=2, y=3

Solve:
x + y = 4
-5x - 6y = -18

• (6, -2)

• (-6, 10)

• (2, 2)

• (-2, 6)

7. Solve the system of linear equations: 2x + 5y = 13 and 3x - 2y = 4

• x = 4, y = 4

• x = 3, y = 1

• x = 2, y = 3

• x = 5, y = 2

10. Solve the following system of equations: 5x - 4y = 3 and 2x + 3y = 8

• x = 4, y = 3

• x = 2, y = 1

• x = 3, y = 2

• x = 1, y = 5