Rational Equations, Solving Via Systems Method

Rational Equations, Solving Via Systems Method

by Denae McNeily

​What is a Rational Equation?

A rational equation is an equation containing AT LEAST one fraction whose numerator (top number) and denominator (bottom number)​

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These fractions may be on one or both sides of the equation.

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​Examples of Rational Equations

​(ONE WAY) To solve:

​Enter the left side of the problem into y₁.

​Enter the right side of the problem into y₂.

​

​Use equation intersection to find the solution.

Multiple Choice

Solve:

• x = 6
• x = -6
• x = 6/7
• x = -6/7

Multiple Choice

Solve:

• x = 2
• No Solution
• x = -10
• x = 10

Multiple Choice

Solve:

• x = -1, 5
• No Solution
• x = -4, 5
• x= -4

Multiple Choice

Solve:

• x = 4/3
• x = 2
• x = 3/4
• x = 2/3

Multiple Choice

Solve:

• x = 0, 5/2
• x = 5/2
• x = 0
• No Solution

Multiple Choice

Solve:

• x = 1
• x = -3
• x = 0 
• x = 3

Multiple Choice

Solve:

• 6
• 17/5
• 19/2
• - 6

Multiple Choice

Solve:

• - 7/6
• - 9/5
• 9/5
• -3

Multiple Choice

Solve:

• 5
• - 5, 4
• - 5
• 5, 4

Multiple Choice

Solve for x

• 5/3, 1
• - 5, 1
• 5, 2/3
• 5, 1

Multiple Choice

Solve:

• x = -3
• x = -3, 5
• x = 3, 5
• x = 5

Multiple Choice

Solve:

• x = 10
• x = -30/13
• x = 6
• no solution

Multiple Choice

Working alone at a constant rate, Carla can wash a load of dishes in 42 minutes. If Carla works together with Dan and they both work at constant rates, it takes them 28 minutes to wash the same load of dishes. Working at a constant rate, how long would it take Dan to wash the load of dishes by himself?

• 50 minutes

• 1 hour

• 84 minutes

• 2 hours

Multiple Choice

Working alone, it takes Asanji eight hours to dig a 10 ft by 10 ft hole. Brenda can dig the same hole in nine hours. How long would it take them if they worked together?

• 2 hours

• 4 hours

• 4.24 hours

• 5 hours

Multiple Choice

Our dog had 6 puppies. We gave away 4. We kept the rest. How many puppies do we have left?

• 2

• 10

• 8

Multiple Choice

Sheyenne has 23 marbles. Jessica has 5 more marbles than Sheyenne does. How many marbles does Jessica have?

• Multiply

• Divide

• Subtract

• Add

Multiple Choice

Dante bought a car for $5,677. Malachi bought his car for $10,987. What is the difference in the cost of the 2 cars?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

Hamburger meat sells for $6 for every 3 pounds. If Alicia buys 10 pounds of hamburger meat, how much will she pay?

• $30
• $20
• $60
• $10

Multiple Choice

If a man runs at a speed of 70 m/s, and has a time of 30 s. What is the distance he ran?

• 2100 m
• 0.233 m
• 2.33 m
• 300m

Multiple Choice

Lee charges $3 for a basket and $2.50 for each pound of fruit picked at the orchard. Write an equation in y = mx + b form for the total cost of x pounds of fruit from the orchard.

• y = 3x + 2.5
• y = 2.50x + 3
• y = 2.50x 
• y = 3x + 2.50

Multiple Choice

You plan to go snowboarding. The resort charges $15 an hour in addition to $25 to rent a board. Write an equation that represents the cost to go snowboarding for the day.

• y=15x-25
• 15x+25y=100
• 25x+y=15
• y=15x+25

Multiple Choice

A man is climbing down from 100 feet high descending 30 feet per minute.

• y = 100 - 30x
• y = 100 + 30x
• y = 100x + 30
• y = 100x - 30

Multiple Choice

Jenny went to the sale at Kohl's last weekend.  
T-shirts were on sale for $15 each and hoodies were on sale for $20 each.  If she spent $150 total, write an equation to represent this situation.  

• 20x + 15 = y 
• 35x = y 
• 15x + 20y = 150 
• 150 - 20x = 15y 

Multiple Choice

Sam ordered 4 tacos and 5 enchiladas for lunch at the restaurant. His bill came to $10.80. Which equation matches the given situation?

• 4x + 3y = 8.10

• 4x + 5y = 10.80

• 4x - 5y = 10.80

• 4x + 10.80y = 5

Multiple Choice

A holiday meal costs $12.50 a person plus a delivery fee of $30.  Which equation represents the amount a holiday meal costs, including delivery, for x people?

• y = 30 + 12.5x 
• y = 12.5 + 30
• y = 12.5 + 30x