Free Printable MA 150 CC Linear Models, Systems of Equations

Worksheets

MA 150 CC Linear Models, Systems of Equations

Total questions: 70

Worksheet time: 6hrs 50mins

Name

Class

Date

w=g+7
solve for g

g=w/7

g=w+7

g=7w

g=w-7

S=6n-12
solve for n

n=(S/6)+2

n=(S/6)+1/2

n=(S/2)+6

n=6S+12

2m-6=4n
solve for n

n=1/2m-3/2

n=6+2m

n=3/2+1/2m

n=4m+6

ax+r=7
solve for r

r=7/ax

r=7-ax

r=7+ax

r=7ax

(x/5)-g=4
solve for x

x=20+5g

x=(4+g)/5

x=5g+4

x=4g+5

Solve the literal equation for the given variable.

2A/h

2/(h)

2Ah

Ah/2

Solve for x:

ax - b = cx + d

x = (a-c)/(b+d)

x = (b+d)/(a-c)

x = (b+d)/(a+c)

x = (a+c)/(b-d)

T = PV/K

T = PK/V

T=KV/P

Greenland

What is the standard form for a Quadratic?

ax²+ bx = - c

x = -b ± √(b²-4ac) / 2a

ax² + bx + c

y = mx + b

10.

What is name of the graph of a Quadratic Equation?

Line

Parbola

Parabola

11.

What are the solutions? List the x-values.

-2, 1

1, 2

-1,2

0,-4

12.

Solve the equation using square roots.
x² = 121

60.5

± 11

± 12

13.

Solve the equation using the zero product property.
(x- 9)(x + 3) = 0

x = 3 or x = 9

x = 3 or x = -9

x + -3 or x = 9

x = -3 or x = -9

14.

Solve the equation using the zero product property.
3x ( 2x - 4) = 0

x = -1/3 or x = -2

x = 0 or x = 2

x = 0 or x = -2

x = -1/3 or x = 2

15.

Solve the equation by factoring.

x² + 13x -y = - 40

x = -8 and x = 5

x= -40 and x = -1

x= 5 and x = 8

x= -8 and x= -5

16.

Solve the equation by factoring. The graph of:

f(x) = x² - 35x - 36 crosses the x-axis at:

-1, 36

1, -36

-6, 6

-6

17.

Factor x²-6x-40

(x-10)(x+4)

(x+10)(x-4)

(x-8)(x+5)

(x+8)(x-5)

18.

Solve, what are the zeros find the roots.

f(x) = x² + 13x + 12

x = -12, -1

x = 12, 1

x = 13, 1

x = -13, -1

19.

f(x) =ax²+bx+c is the standard form of a quadratic equation.

True

False

20.

What should you do first in solving this equation?
x² + 6x - 13 = 3

Get factored form

Write down: a=1, b=6, c=-13

Make it equal 0 by subtracting 3 on each side

Type it all in a calculator.

21.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a = 4, b = -8, c = 3

a = 4, b =-8, c =-3

a = 4, b = 8, c = 3

a = 4, b = 8, c = -3

22.

Solve the equation:
5x² - 35x + 60 = 0

x = 3, -4

x = -3, 4

x = 3, 4

x = -3, -4

23.

Solve the equation:
4x²+2x - 6 = 0

x = 1 & -1.5

x = -1 & 1.5

x = (-2 ±√92)/8

x = (-2 ± √100)/8

24.

What is the vertex of the graph?

(2, 4)

(3, -1)

(0, 8)

(4, 2)

25.

What is the solution?

(1, -1)

(-1, 1)

(0, -2)

(2, 0)

26.

^{What is the solution?}

-2

(1, 2)

(1, -1)

27.

When you graph the exact same equation twice,

you will have no solution.

you will have one solution.

you will have infinite solutions.

you will graph a giraffe.

28.

How many solutions will this system have?

No solution

One Solution

I Don't Know

Infinitely Many Solutions

29.

Does the system have one, none or infinite solutions?

8x + 4y = 12

y = -2x + 3

One Solution

No Solution

Infinitely Many Solutions

30.

Solve for x and y
5x + 3y = 7
y = 4

(4,1)

(4,-1)

(1,4)

(-1,4)

31.

If a system of equations has infinitely many solutions, what does the graph look like?

intersecting lines

parallel lines

the same line (coinciding lines)

32.

4x+8y=20
-4x+2y=-30

(-7,1)

(2,-5)

(-2,5)

(7,-1)

33.

Solve the System of Equations by Substitution: 4x + 6y = 16 and x = -2

(-2, 1)

(-2, 4)

(-2, 2)

34.

What would be the first step in finding the solution using elimination?

2x + 2y = -2

3x - 2y = 12

you cannot solve this using elimination

cross out the 2x and 3x

cross out the 2y and -2y

change to slope intercept form and graph

35.

The solution to a system of equations is any ordered pair that makes both equations true.

TRUE

FALSE

36.

Solve with substitution

x = -3y - 8

x - 2y = -3

(5, -1)

(-5, 1)

(-5,-1)

(1,-5)

37.

Solve using substitution:

y = -6x + 5

-2x + y = 5

(-3, -6)

(-6, 3)

(0, 5)

(-3, 5)

38.

Solve by elimination
-2x + 6y = 16
-4x - 3y = 2

(2,2)

(-2, -2)

(-2,2)

(2,1)

39.

Solve using elimination.
4x + 8y = 20
-4x + 2y = -30

(-7,1)

(2,-5)

(-2,5)

(7,-1)

40.

You can solve systems using these methods:

graphing, substitution, and elimination

rearranging, thinking, and guessing

only by graphing

41.

Solve by elimination:
7x+y=-9

-3x-y=5

No solution

(1,8)

(-2,-3)

(-1,-2)

42.

Write the equation of the line.

y = -1/3x - 2

y = 1/3x - 2

y = 3x - 2

y = -3x - 2

43.

Write the equation of the line.

y = -2/3x + 4

y = 2/3x + 4

y = 3/2x + 4

y = -3/2x + 4

44.

If you where to graph the equation y = 2x - 3, how would you begin?

By going up 2 and over 1

By placing a point at -3 on the y-axis

By going down 2 and over 3

By going up 2 and over 3

45.

How would you graph y = ¹/₂ x + 2

Allow your pencil to aimlessly drift across your paper until- Behold! A line is formed!

Place a point at 0.5 on your y-axis. Then go up 2 and right 1 and place your second point. Draw your line.

Start at the origin and go down 1 and over 2 again and again until you see your line.

Place a point at 2 on the y-axis. Then from that point go up 1 and right 2 and place your second point. Draw your line. (Or make a t-chart)

46.

The solution (x, y) to a system of equations is the point where they...?

Run off the graph

Don't touch

Intersect

Exist

47.

If a system of linear equations has one solution, what does this mean about the two lines?

Parallel lines

the same line

Intersecting lines

48.

Is (1,10) a solution to

y=7x+5

y=x+9

yes

49.

Is (1,7) a solution for

y=3x+4

y=x+6

yes

50.

HOW is a coordinate pair ordered, ALWAYS?

(big number, small number)

(small number, big number)

(y, x)

(x, y)

51.

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount?

y = 6.80 + .65x
y=7.30+.90x

x + y = 6.80
x + y = 7.30

y = 6.80+.90x
y = 7.30 + .65x

y + .90x = 6.80
y + .65x = 7.30

52.

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

y = 9.65 + x
y = 8.40 + x

y = 9.65x + 43
y = 8.40x + 58

y =9.65x
y = 8.40x

y = 9.65x - 43
y = 8.40x - 58

53.

What does break even point show?

where a business is neither making a profit or loss

how many items to make

how much profit they're making

where a business has more fixed costs than variable

54.

What assumption does this statement say "Break even is 54 units"?

if we sell 55 we aren't making a profit

if we sell 54 we begin to make a profit

if we sell 55 we begin to make a profit

if we sell 54 we are not yet at break even point

55.

To draw the BE graph you must plot Total Costs and ........

Total Production

Total Revenue

Total Fixed Costs

Total Units

56.

Businesses calculate break-even in units so they know

how much profit they will earn after they break even

which products they should purchase for resale

which costs are variable and which are fixed

how many products they must sell to break even

57.

Brady and Ja invest $2700 to start a hair cutting business. Each hair cut costs them $1.50 (supplies). They charge their customer $15 for each cut.

Write the equation for cost and income.

Cost: y = 1.50x + 2700

Income: y = 15x

Cost: y = 150 + 2700

Income: y = 1.50x

Cost: y = 1.50x + 2700

Income: y = 15

Cost: y = 2700

Income: y = 15x + 1.50

58.

Tyrone and Tom Brady invest $2700 to start a hair cutting business. Each hair cut costs them $1.50 (supplies). They charge their customer $15 for each cut.

How many hair cuts until they breakeven?

200 hair cuts

22 hair cuts

2700 hair cuts

59.

Adam and Levi invest $2700 to start a hair cutting business. Each hair cut costs them $1.50 (supplies). They charge their customer $15 for each cut.

How much profit will they make if they sell 344 haircuts?

(income - cost = profit)

$1,944

$1940

$340

340 hair cuts

60.

At a local ballpark a team charges $10 per ticket. The team must pay its players $4000. It costs the owners $6 for each souvenir they give away.

Write an equation for cost and income.

cost: y = 6x + 4000

income: y = 10x

cost: y = 10x + 4000

income: y = 6x

cost: y = 10x + 4000

income: y = 6

cost: y = 4000x + 10

income: y = 6x

61.

At a local ballpark a team charges $10 per ticket. The team must pay its players $4000. It costs the owners $6 for each souvenir they give away.

How many tickets must be sold to break even.

1000 tickets

10,000 tickets

600 tickets

660 tickets

62.

At a local ballpark a team charges $10 per ticket. The team must pay its players $4000. It costs the owners $6 for each souvenir they give away.

How much profit will they make if they sell 2,230 tickets?

(income - cost = profit)

$2,230

$4,920

$1,000

$2, 920

63.

At a local concert hall, the owner charges $7 per ticket. The owner must pay his band $1200. Every customer receives a brochure that costs the owner $2 for each person.

How many people must attend for him to breakeven?

240 people

170 people

600 people

133 people

64.

At a dinner theatre the owner charges $25 per ticket. She pays her employees $18,500. Each customer leaves with a free dessert that cost the owner $5 per dessert.

When will the owner break even?

925 customers

740 customers

18500 customers

3700 customers

65.

At a local concert hall, the owner charges $7 per ticket. The owner must pay his band $1200. Every customer receives a brochure that costs the owner $2 for each person.

Write an equation for cost and income

Cost: y = 2x + 1200

Income: y = 7x

Cost: y = 7x + 1200

Income: y = 2x

Cost: y = x + 1200

Income: y = 7

Cost: y = 2x + 7

Income: y = 1200x

66.

(Simple Interest)
What was the interest rate if your balance on an investment of $830 at the end of one year is $871.50?

41.5%

67.

(Simple Interest)
How much interest is earned on $140 at 7% for five years?

20%

$49

49%

68.

(Simple Interest)
The ending balance on an investment is $1,620.24. If the principal was invested at 8% for nine years, what was the principal?

$492

$129.62

$942

$192.69

69.

(Simple Interest)
How much principal must be invested to earn $403.20 in seven years at an interest rate of 9%?

$36.29

$640

70.

(Simple Interest)
How long must $217 be invested at a rate of 6% to earn $78.12 in interest?

6 years

4 years

8 years

2 years

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MA 150 CC Linear Models, Systems of Equations

Total questions: 70

Worksheet time: 6hrs 50mins

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