Chapter 6 Review: Systems of EquationsHonors Math – Grade 8

Important VocabularySystems of equationsElimination using Addition/SubtractionIntersecting and Parallel LinesSubstitution

Use the graph to determine whether each system is consistent or inconsistent and if it is independent or dependent.

The following table states the best time to use a method for solving a system of equations.

Choose the best method and solve each system of equations.

Choose the best method and solve each system of equations.

Choose the best method and solve each system of equations.

At a sale, Sarah bought 4 T-shirts and 3 pairs of jeans for $181. Jenna bought 1 T-shirt and 2 pairs of jeans for $94. The T-shirts were all the same price and the jeans were all the same price. How much did each item cost?

Let t = the cost of a t-shirt and j = the cost of

jeans..

Define the Variables

Write a system of equations.

4 t-shirts + 3 jeans = 181

4t + 3j = 181

1 t-shirt + 2 jeans = 94.

1t + 2j = 94

942118134

jtjt

1. Write the equations in column form. Multiply to eliminate a variable.

942118134

jtjt

4( )

The t variable is eliminated because

4 - 4 = 0

1955 j j = 39

3768418134

jtjt

Distribute

A t-shirt costs $16 and a pair of jeans cost $39.

2. Since the coefficients of t are 4 & 4 (the same), subtract the equations.

t + 2j = 94

t + 2(39) = 94

t + 78 = 94

t = 16

Solve the equation

3. Now substitute j = 39 in either equation and solve.

-

In 2000, the number of film cameras sold was 20 million and the number of digital cameras sold was 4.7 million. Since then, the number of film cameras has decreased at an average rate of 2.5 million per year and digital cameras has increased at an average rate of 2.6 million per year. In how many years will the sale of digital cameras equal the sale of film cameras?

Let y = the number of cameras sold and x = the number of years

after 2000.

Define the Variables

Write a system of equations.

Film decreased 2.5 per yr.

y = 20 – 2.5x

Digital increased 2.6 per yr

y = 4.7 + 2.6x

xyxy6.27.45.220

1. Write the equations in column form. You may eliminate if equations are not in standard form

xyxy6.27.45.220

The y variable is

eliminated because 1

- 1 = 0

x1.53.150

x = 3

In 3 years (or 2003), the number of digital cameras sold will equal the number of film cameras sold.

2. Since the coefficients of y are 1 & 1 (the same), subtract the equations.

Solve the equation

-

3.151.5 x

2335)11(323353

ppps

Denzel sold 25 pizzas and 36 subs.

Substitute p + 11 for s in the first equation.

Distribute and group like terms.

2335333 pp

p = 25

2. Now substitute p = 25 in either equation and solve.

s = p + 11

s = 25 + 11

s = 36

One equation is solved for s; Substitute s= p+11

For the Future Teachers of America fund-raiser, Denzel sold subs for $3 and pizzas for $5. He sold 11 more subs than pizzas and earned a total of $233. How many pizzas and subs did he sell?

Let s = the number of subs sold & p = the number of pizzas sold.

Define the Variables

Write a system of equations.

Earned a total of $233.

3s + 5p = 233

He sold 11 more subs than pizzas.

s = p + 11

1123353

psps

Solve.

233338 p2008 p

65.4114977.3269

nana

Aluminum cans cost $0.01 per pound and newspapers cost $0.39 per pound

The a variable is eliminated

because 9 – 9 = 0

88.088 n n = .01

2. Since the coefficients of a are 9 & 9 (the same), subtract the equations.

9a + 26n = 3.77

9a + 26(.01) = 3.77

9a + .26 = 3.77

9a = 3.51

a = 0.39

1. Write the equations in column form.

Mara recycled 9 pounds of aluminum cans and 26 pounds of newspapers and earned a total of $3.77. Ling recycled 9 pounds of aluminum cans and 114 pounds of newspaper and earned a total of $4.65. What was the price per pound of each?

Let a = the cost of aluminum n = the cost of newspaper.

Define the Variables

Write a system of equations.

9 lbs aluminum & 26 lbs news = 3.77

9a + 26n = 3.77

9 lbs aluminum & 114 lbs news=4.65

9a + 114n = 4.65

65.4114977.3269

nana

-

Solve the equation

3. Now substitute n = .01 in either equation and solve.