System of Equations

Word Problems

100

A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many of each animal are there?

2 ducks and 8 pigs

200

The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

1500 children 700 adults

300

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice and True/False questions are on the test?

5 multiple choice questions 15 T/F questions

400

A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totaled $487. The second order was for 6 bushes and 2 trees, and totaled $232. The bills do not list the per-item price. What were the costs of one bush and of one tree?

One bush cost $23 each; one tree cost $47 each.

500

Margie is responsible for buying a week's supply of food and medication for the dogs and cats at a local shelter. The food and medication for each dog costs twice as much as those supplies for a cat. She needs to feed 164 cats and 24 dogs. Her budget is $4240. How much can Margie spend on each cat and dog for food and medication?

She can spend $20 on each cat and spend $40 on each dog.

Vocabulary

100

What are the definitions of one, no, and infinite solution situations?

One Solution- One point of intersection, one answer, different slopes No Solution- No point of intersection;parallel lines, same slopes, different y-intercepts. Infinite Solutions- all points in common, same slopes, same y-intercepts, same line

200

y=23x+70 60x+12y=144 What is the best solution to this system and when is the best time to use it?

Substitution Substitution is best used when another variable in a system is isolated.

300

Create a sentence of the best method to solve this system and when is the best time to use this method? 7x+13y=89 12x-5y=64 DO NOT SOLVE!!

The best way of solving this problem is Elimination. Elimination is most helpful when the y-intercept is isolated.

400

A system of equations is a set of _____ that have some type of __________ or none at all.

graphs; relationship

500

A no solution situation: y=0 I am a line that intersects this straight line twice. I cannot be put into slope-intercept form. What am I? (hint:U ---)

A Parabola.

Methods

100

Solve by using ONLY elimination. 2x + 2y=6 12=2y - x

(-2,5)

200

Solving this by using substitution solving for "x" 4x+6y=82 y=3

x=16

300

Solve this system by using substitution. 4x+7y=93 y=3x+28

x=-4.12 y=15.64

400

Solve this using any system to find "x" and "y" 20x+40y=450 6x+256=8y

x=-16.6 y=19.55

500

Solve this using elimination to find "x" and "y" DO NOT ROUND. 3x+4y=83 6y=-8.5x+106.5

x=-4.5 y=24.125

Identifying Solutions and Methods

100

On google presenation ....

From left to right, the first one is one solution, the second one is infinite solution, and the third one is no solution.

200

Give examples of one, no, and infinite solutions in the form of a system.

One solution 2x+3y=12 4x+5y=20 y=4 x=0 No Solution y=2x+2 y=2x+-5 Infinite Solution 4x+2y=40 2x+y=20

300

Identify the best and worst methods to solving the system of equations. 3x+2y=4 5x-4y=3

Best: Elimination Worst: Substitution

400

Solve this system of equations 10x+11y=111 12x+15y=210 If there is a decimal put the first two numbers after the decimal point. DO NOT ROUND!

y=92.66 x=-90.826

500

Rose accidentally ripped an important part of a problem she did for homework. All she had was y=2x+? 4x+?y= 149 What could the question marks possibly be in order to get a solution of (7,11)?

1st ?= -3 2nd ?= 11

Miscellaneous

100

David came across a system of equations on his test review. 6x+7y=72 5x+4y=135 He did the easiest method. What was it?

Elimination

200

Wolfrich lived in Portugal and Brazil for a total period of 14 months in order to learn Portuguese. He learned an average of 130 new words per month when he lived in Portugal, and an average of 150 new words per month when he lived in Brazil. In total, he learned 1920 new words. How long did he live in each?

He lived in Portugal for 9 months and lived 5 months in Brazil.

300

When you use _______, you want to line up the ______ and eliminate _ variable.

Elimination, variables, one

400

y =36–9x 3x+y/3=12 Solve using ONLY Substitution.

y=36–9x

500

Double OR Nothing. Choose whether you want to take this chance! Either double it all or reduce all your points to zero. Your choice! y=14x+8 7x+9y=525 1. Solve. You are allowed to use both substitution and elimination. 2. Also, change the slope for the first equation so that y=48. Use the x-value from the first part of your answer.

1. x=5 y=36 2. y=8x+8