Linear Equations
System of Linear Equations (substitution)
Find the GCF
Growth and Decay
100

Solve for X; 

3x + 5 = 11

x = 2

100

Solve this equation with substitution;
y= 6x + 7

3x - 8y = 4

(-4/3, -1)

100

Find the GCF;

15x2 + 18

GCF = 3

100

You earn $11 per hour and receive an average annual pay raise of 8%. What would you expect your hourly wage to be in 12 years?

$27.70

200

Solve for X;

2x = 7 + 3y

x = 7+3y/2

200

Solve this equation with substitution;

y = 2x - 1

2x + 3y = -7

(1,3)

200

Find the GCF;

-18y4  + 6y3 + 24y2

GCF = 2y2

200
You earn $10 per hour and receive an average annual pay raise of 5%. What would you expect your hourly wage to be in 5 years?

$12.76

300

Solve for X;

5x + 8 = 3x - 2

x = -5

300

Solve this equation with substitution;

x = y + 6

x + y = 10

(8,2)

300

Factor out GCF;

x3 + 5x2 - 22x

} x(x2 + 5x - 22)

300
You invest $30,000 in a mutual fund that averages approximately 8% annual growth with semi-annual compounding periods. You decide to leave the money for retirement for 30 years. Assuming the initial $30,000 is your only investment, how much money do you expect this fund to have by retirement?

$315,588.82

400

Solve for X;
2x + 5 = 12x + 1

x = 2/5

400

Solve this equation;

x + y = - 4 

y = -x + 5

(-5,1)

400

Factor out GCF;

-16y6 = 28y4 - 20y3

} -4y3 (4y3 - 7y + 5)

400

You live in a small rural town with a population of 1000 people. On average, the town experiences a 2% annual decline in population. How many people would you expect to live in your town in 5 years?

903 people

500

Solve for X;
3x - 7 = 2(4x+5) - 9

  x = 8/5

500

Solve this equation with substitution;

y = 6 - x

4x - 3y = -4


(2,-5)

500

Factor out GCF;

3x3y2 - 9xz4 + 8y2z

No common factor

500

You acquire a house initially appraised at $200,000, and its value increases by 5% annually for the first 6 years. Then, it decreases in value by 3% for the following 4 years. How much do you expect this house to be worth 10 years after you acquire it?

$237,275.29

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