Substitution Stumpers
Solve by Substitution:
4x + 2y = 14
y = 2x - 1
What is x = 2, y = 3?
Solve by Elimination:
6x + 4y = 20
2x − y = 2
What is x = 2, y = 2?
6x − 5y = 8
−12x + 2y = 0
What is x = -1/3, y = -2?
Joanna has two dogs, Rover and Spot, who weigh a combined total of 87 pounds. If Rover weighs 9 pounds more than Spot, how many pounds does Spot weigh?
What is 39 pounds?
The sum of 4 times a larger integer and 5 times a smaller integer is 7. When twice the smaller integer is subtracted from 3 times the larger, the result is 11. Find the integers.
What is 3 and -1?
4x - 2y = 10
y = 3x - 2
What is x = -3, y = -11?
Solve by Elimination:
2x + y = 10
4x − 2y = 8
What is x = 7/2, y = 3?
x − 7y = −11
5x + 2y = −18
What is x = -4, y = 1?
A sporting good store sells one type of baseball bat and one type of baseball. The cost for 2 bats and 4 balls is $160. The cost for 1 bat and 6 balls is $160, as well. If someone were to buy an equal number of bats and balls, at most how many bats can he purchase if he has a budget of $240 for the purchase?
What is 4?
Joey has a jar full of 40 coins consisting of only quarters and nickels. If the total value is $5.00, how many of each coin does Joey have?
What is 15 quarters and 25 nickels?
Solve by Substitution:
3x + 2y = 18
x − y = 6
What is x = 6, y = 0?
Solve by Substitution:
2x + 3y = 17
3x − 2y = 6
What is x = 4, y = 3?
4x − 2y = 10
y = 3x − 2
What is x = -3, y = -11?
Molly's school is selling tickets to a dance performance. On the first day of ticket sales, the school sold 9 adult tickets and 12 child tickets for a total of $183. The school took in $160 on the second day by selling 12 adult tickets and 4 child tickets. What is the price each of one adult ticket and one child ticket?
What is Child: $7, Adult: $11?
A jar consisting of only nickels and dimes contains 58 coins. If the total value is $4.20, how many of each coin is in the jar?
What is 32 nickels and 26 dimes?
Solve by Substitution:
4x+3y=14
y = x + 1
What is x = 11/7, y = 18/7?
Solve by Elimination:
2x+4y=10
4x+8y=20
What are infinite solutions?
x + 8y = 18
2x − 4y = −6
What is x = 6/5, y = 21/10?
Jason and Mallorie are selling baked goods for a school fundraiser. Students can buy boxes of assorted donuts and boxes of cupcakes. Jason sold 3 boxes of donuts and 14 boxes of cupcakes for a total of $178. Mallorie sold 14 boxes of donuts and 6 boxes of cupcakes for a total of $178. What is the cost each of one box of assorted donuts and one box of cupcakes?
What is Donuts: $8, Cupcakes $11?
Consider the system:
4x + ky = 20
2x - 3y = 10
Find a value of k such that the system has infinitely many solutions.
What is k = 6?
Solve by Substitution:
7x − 2y = 14
3x + y = 9
What is x = 32/13, y = 21/13?
Solve by Elimination:
x − 2y = 4
3x − y = 6
What is x = 8/5, y = -6/5?
−2x + 10y = 25
5x − 25y = 3
What is no solution?
The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
What is Van: 8, Bus: 22?
A 1.8% saline solution is to be combined and mixed with a 3.2% saline solution to produce 35 ounces of a 2.2% saline solution. How much of each is needed?
What is 1.8% Solution: 25 Ounces, 3.2% Solution: 10 Ounces?