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Solving systems of equations with 2 variables. Word problems (Number Problems). 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.

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Solving systems of equations with 2 variables

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## Solving systems of equations with 2 variables

Word problems

(Number Problems)

### 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