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Graphing
Substitution
Elimination
Section 5.4
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100

Where does the two lines intersect?

x + 2

-x + 4


Point (1,3)

100

Solve the system of linear equations by substitution.

y = 2x+ 3

y = 5x

(1,5)

x = 1

y = 5

100
Solve by using elimination.

3x + 4y = -6

7x + 4y = -14

(-2,0)

100

Solve the system of linear equations.

x = 2y + 10

2x + 3y = -1

(4,-3)

100

Solve for c

19 - 4c = 17

c = 0.5

200

What are the y-intercepts and point of intersection?

3x - 3

2x

y-intercepts: (0,0) (0,-3)

point of intersection: (3,6)

200

Solve the system of linear equations by substitution.

4x + 2y = 0

y = -0.5x - 5

(2,-4)

200

2x + 5y = 16 

3x - 5y = -1

(3,2)

200

y = 1/3 x + 1

-x + 3y = -6

no solution

200

Solve for x

1.1x + 1.2x - 5.4 = -10

x = -2

300

What are the y-intercepts and point of intersection?

2x + 4

6x - 7

y-intercepts: (0,4) (0,-7)

point of intersection: (2.75,9.5)

300

Solve using substitution.

y = 2x + 5

y = 3x - 1

(6,17)

300

4x - 5y = -19

-x - 2y = 8

(-6,-1)

300

y = - 1/6 x + 5

x + 6y = 30 

infinitely many solutions; all points on the line

y = - 1/6 x + 5

300

Write in slope-intercept form an equation for the line that passes through the given points.

(-9,5), (-3,3)

y = -1/3 x + 2

400

Give the equations for the lines on the graph.

y=-4x-7

x+y=2 or y=-x+2

400

An animal shelter has a total of 65 abandoned cats and dogs. The ratio of cats to dogs is 6:7. How many cats are in the shelter? How many dogs are in the shelter?

30 cats, 35 dogs

400

5x = 4y + 8 

3y = 3x - 3

(4,3)

400

-2x + y = 1.3

2(0.5x - y) = 4.6

(-2.4,-3.5)

400
You have 500 sheets of notebook paper. After 1 week, you have 72% of the sheets left. You use the same number of sheets each week. 


Write an equation that represents the number y of pages remaining after x weeks. 

y = -140x + 500

500

Write an equation that represents the costs. Write an equation that represents the revenue. Find where the two lines intersect.

Your family starts a bed and breakfast. it spends $500 fixing up a bedroom to rent. the cost for food and utilities is $10 per night. Your family charges $60 per night to rent the bedroom. 

Cost: y=10x+500

Revenue: y=60x

point of intersection: (10,600)

500
A drama club earns $1040 from production. It sells a total of 64 adult tickets and 132 student tickets. An adult ticket cost twice as much as a student ticket.

Write a system of linear equations.

What is the cost of each ticket?

x = 2y

64x + 132y = 1040

adult = $8

student = $4

500

You can jog around your block twice and the park once in 10 minutes. You can jog around your block twice and the park 3 times in 22 minutes. 

Write a system of linear equations.

How long does it take to jog around the park?

2x + y = 10 

2x + 3y = 22

It takes 6 minutes.

500

You downloaded a digital album for $10. Then you and your friend downloaded the same number of individual songs for $0.99 each. 

Write a system of equations for the situation. 

Will you and your friend spend the same amount of money?

y = 0.99x + 10

y = 0.99x

no because you paid $10 before buying the same number of songs at the same price, you spend $10 more

500

If there were ten fish in an enclosed tank, and four swam away, three died, and three drowned, how many fish would be left?

Seven fish, fish can't drown and can't swim away in a tank