Quiz

Intro Video

Solving a System of Equations Using Substitution

Today, we are going to solve the equations we wrote last time using substitution.

The volleyball club has 41 members. There are 3 more boys than girls. How

many girls are there?

Identify your variables. boys = b

girls = g

The volleyball club has 41 members. b + g = 41

There are 3 more boys than girls. b = g + 3

Now your system is set-up!

b + g = 41

b = g + 3

• Solve one of the equations for one of the variables

• Substitute it into the other equations.

• Solve for the remaining variable

• Substitute that answer back into one of the original equations and solve.

• b = g + 3

• g + 3 + g = 41

• 2g + 3 = 41

- 3 -3

2g = 38

2 2

g = 19

• b = 19 + 3

b = 2219 girls

22 boys

A rectangle has a perimeter of 18 cm. Its length is 5 cm greater than

its width. Find the dimensions.

Identify your variables. Length = l

Width = w

A rectangle has a perimeter of 18 cm. 2l + 2w = 18

Its length is 5 cm greater than its width. l = 5 + w

Now your system is set-up!

• Solve one of the equations for one of the variables

• Substitute it into the other equations.

• Solve for the remaining variable

• Substitute that answer back into one of the original equations and solve.

• l = 5 + w

• 2(5 + w) + 2w = 18

• 10 + 2w + 2w = 18

10 + 4w = 18

-10 -10

4w = 8

4 4

w = 2

• l = 5 + 2

l = 7

Width = 2

Length = 7

2l + 2w = 18

l = 5 + w

Timmy has 180 marbles, some plain and some colored. If there are 32 more plain marbles than colored marbles, how many colored

marbles does he have?

Identify your variables. Plain marbles = p

Colored marbles = c

Timmy has 180 marbles. p + c = 180

If there are 32 more plain marbles than colored marbles.

p = c + 32

Now your system is set-up!

• Solve in your groups/on your own

p + c = 180

p = c + 32

The sum of two numbers is 15. Twice one number equals 3 times

the other. Find the numbers.

Identify your variables. First Number = x

Second Number = y

The sum of two numbers is 15. x + y = 15

Twice one number equals 3 times the other. 2x = 3y

Now your system is set-up!

• Solve one of the equations for one of the variables

• Substitute it into the other equations.

• Solve for the remaining variable

• Substitute that answer back into one of the original equations and solve.

• x + y = 15

-x -x

y = -x + 15

• 2x = 3(-x + 15)

• 2x = -3x + 45

+3x +3x

5x = 45

5 5

x = 9

• 9 + y = 15

-9 -9

y = 6

1st number is 9

2nd number is 6

x + y = 15

2x = 3y

The sum of two numbers is 36. Their difference is 6. Find the

numbers.

Identify your variables. First Number = x

Second Number = y

The sum of two numbers is 36. x + y = 36

Their difference is 6. x - y = 6

Now your system is set-up!

• Solve in your groups/on your own

x + y = 36

x - y = 6

A theater sold 900 tickets to a play. Floor seats cost $12 each and balcony seats $10 each.

Total receipts were $9780. How many of each

type of ticket were sold?

Identify your variables. Floor seats = f

Balcony seats = b

A theater sold 900 tickets to a play. f + b = 900

Floor seats cost $12 each and balcony seats $10 each. Total receipts were $9780

12f + 10b = 9780

Now your system is set-up!

• Solve in your groups/on your own

f + b = 900

12f + 10b = 9780

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