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Solve by Graphing

Solve by Substitution

Solve by Elimination

Systems of Inequalities

Word Problems

Kickin’ it up a notch

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100 Points

Answer

Solve the system by graphing:

NO SOLUTION, lines are parallel

Template by

Bill Arcuri, WCSD

200 Points

Answer

Solve the system by graphing:

2y = -4x + 4

Y = -2x + 2

Infinite Solutions (same lines)

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Bill Arcuri, WCSD

200 Points

Solve the system by substitution:

x = -4y

3x + 2y = 20

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Bill Arcuri, WCSD

500 Points

Solve the system by substitution:

Tickets to a movie cost $7.25 for adults

And $5.50 for students. A group of

Friends purchased 8 tickets for $52.75.

How many adult and student tickets were

Purchased?

500 Points

Answer

a + s = 8

7.25a + 5.50s = 52.75

5 adult and 3 student tickets sold.

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Bill Arcuri, WCSD

100 Points

Answer

Solve by elimination:

p + q = -2

P – q = 8

(3, -5)

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Bill Arcuri, WCSD

200 Points

Answers

Solve by elimination:

7x + 2y = 2

7x – 2y = -30

(-2, 8)

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Bill Arcuri, WCSD

300 Points

Answer

Solve by elimination:

-4y + x = -2.5

2x + 4y = 10

(2.5, 1.25)

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Bill Arcuri, WCSD

400 Points

Answer

Solve by elimination:

-11x – 10y = 17

5x – 7y = 50

(3, -5)

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Bill Arcuri, WCSD

500 Points

200 Points

Two angles are complementary.

The measures of the two angles

Have a difference of 20 degrees.

What is the measure of each angle?

300 Points

Vignesh has been saving his dimes and

Quarters. He has 94 coins in all, and

The total value is $19.30.

How many dimes and how many

Quarters does Vignesh have?

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Bill Arcuri, WCSD

400 Points

Betty and Bob went on a Safari.

The saw giraffes and ostriches.

When they counted, there were 40

heads, and 130 feet.

How many giraffes and ostriches

Did they see?

Ally and Matt went shopping for

Produce on the same day. Ally bought

8 lbs of apples and 7 lbs of potatoes

For $18.85. Matt bought 2 lbs of apples

And 10 lbs of potatoes for $12.88.

What is the cost of apples and potatoes

Per pound?

Topic 5

500 Points

100 Points

Answer

The solution is the point where

The two lines intersect.

It is the (x,y) value that satisfies

Both equations.

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Bill Arcuri, WCSD

200 Points

Answer

The solution to a system of

Inequalities are all of the points that satisfy both inequalities.

When you graph them, it is the

Section of the graph where shaded sections of the inequalities overlap.

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Bill Arcuri, WCSD

300 Points

Four times one number added to

Another number is 36. Three times

The first number minus the other

Number is 20. Find the numbers.

300 Points

Answer

Four times one number added to

Another number is 36. Three times

The first number minus the other

Number is 20. Find the numbers.

The numbers are: 8 and 4

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Bill Arcuri, WCSD

Topic 6

400 Points

An airplane flying against the wind takes

16 hours to travel 1800 miles. The return

Trip, flying with the wind takes only 9

hours. What is the speed of the airplane

In still air?

Topic 6

400 Points

Answer

Let a = rate of airplane and

Let w = rate of the wind.

9 (a + w) = 1800

16 (a - w) = 1800

a = 156.25 miles per hour

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Bill Arcuri, WCSD

500 Points

A certain systems consists of 2

equations. One of the equations is

½ x + y = 3. Write a second equation

For the system so that the system

Has…

no solutions __________________

Infinite solutions _______________

Exactly one solution ____________

500 Points

Answer

½ x + y = 3 can be rewritten as

y = - ½ x + 3

Answers will vary (samples…)

y = - ½ x + 5 (same slope – parallel)

2y = - x + 10 (same equations – mult by 2)

y = 3x – 2 (any equation with different slope will intersect)

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Bill Arcuri, WCSD

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