Solving Systems of Equations: The Substitution Method

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### Solving Systems of Equations:The Substitution Method

Example 1

Solve using substitution.

y = 3x

2x + 4y = 28

y = 3x

2x + 4(3x) = 28

y = 3(2)

2x + 12x = 28

y = 6

14x = 28

x = 2

(2,6)

REMEMBER To Check:

Always plug solution

into original equations

Example 2

Solve using substitution.

2x + y = 13

4x – 3y = 11

y = -2x + 13

4x – 3(-2x + 13) = 11

4x + 6x – 39 = 11

10x – 39 = 11

10x = 50

x = 5

2x + y = 13

2(5) + y = 13

(5,3)

10 + y = 13

y = 3

Example 3

Solve using substitution. The sum of a number and twice another number is 13. The first number is 4 larger than the second number. What are the numbers?

Let x = the first number

Let y = the second number

x + 2y = 13

y + 4 + 2y = 13

x = y + 4

3y + 4 = 13

3y = 9

y = 3

x = y + 4

x = 3 + 4

x = 7

Practice

Solve using substitution.

2) a – b = 4

3x + 4y = 2

• x + y = 5

x – 2y = 8

b = 2 – 5a

2x – y = 5

x = y + 1

2x + y = 8

3)

4)

Translate to a system of equations and solve.

• The sum of two numbers is 84. One number is three times the other.
• Find the numbers.
Practice

Solve using substitution.

6)

x= ½y + 3

7)

8x + 2y = 13

2x – y = 6

4x + y = 11

Practice

Translate to a system of equations and solve.

5) The sum of two numbers is 84. One number is three times the other. Find the numbers.