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Solving systems of equations with 2 variablesPowerPoint Presentation

Solving systems of equations with 2 variables

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1) The sum of two numbers is 72. Their difference is 40. Find the numbers.

The sum of two numbers is 72.

x + y = 72

Their difference is 40.

x – y = 40

1) The sum of two numbers is 72. Their difference is 40. Find the numbers.

x + y = 72

x – y = 40

Which method should be used to solve this system of equations?

a) Substitution Method

b) Elimination (Addition) Method

1) The sum of two numbers is 72. Their difference is 40. Find the numbers.

Solve using the Elimination (Addition) Method

x + y = 72

x – y = 40

2x = 112

x = 56

Back substitute

56 + y = 72

56 + y + (-56) = 72 + (-56)

y = 16

The numbers are 56 and 16.

2) The sum of two numbers is 21. Their difference is 13. Find the numbers.

Solve using the Elimination (Addition) Method

x + y = 21

x – y = 13

2x = 34

x = 17

Back substitute

17 + y = 21

17 + y + (-17) = 21 + (-17)

y = 4

The numbers are 17 and 4.

3) The sum of two numbers is 27. One number is three more than the other. Find the numbers.

The sum of two numbers is 27.

x + y = 27

One number is 3 more than the other.

y = x + 3

3) The sum of two numbers is 27. One number is three more than the other. Find the numbers.

x + y = 27

y = x + 3

Which method should be used to solve this system of equations?

a) Substitution Method

b) Elimination (Addition) Method

3) The sum of two numbers is 27. One number is three more than the other. Find the numbers.

Solve using the Substitution Method

x + y = 27

y = x + 3

x + (x + 3) = 27

2x + 3 = 27

2x + 3 + (-3) = 27 + (-3)

2x = 24

x = 12

The numbers are 12 and 15.

Back substitution

y = x + 3

y = 12 + 3

y = 15

4) A 36-ft rope is cut into two pieces. One piece is three times the other. Find the length of each piece.

Solve using the Substitution Method

x + y = 36

y = 3x

x + (3x) = 36

4x = 36

x = 9

The pieces are 9 ft and 27 ft.

Back substitution

y = 3x

y = 3(9)

y = 27

5) The difference between two numbers is 3. The larger number is one more than twice the smaller number. Find the numbers.

Solve using the Substitution Method

L – S = 3

L = 2S + 1

(2S + 1) – S = 3

S + 1 = 3

S + 1 + (-1) = 3 + (-1)

S = 2

The numbers are 2 and 5.

Back substitution

L = 2S + 1

L = 2(2) + 1

L = 5

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