Download Solving Systems with Substitution Notes

The Substitution Method
Objectives:
•To solve a system of equations by substituting for
a variable
Example 1
Solve using substitution.
y = 3x
2x + 4y = 28
2x + 4(3x) = 28
2x + 12x = 28
14x = 28
x=2
y = 3x
y = 3(2)
y=6
(2,6)
Practice
Solve using substitution.
1) x + y = 5
x=y+1
2) a – b = 4
b = 2 – 5a
Example 2
Solve using substitution.
2x + y = 13
y = -2x + 13
4x – 3y = 11
4x – 3(-2x + 13) = 11
4x + 6x – 39 = 11
10x – 39 = 11
10x = 50
x=5
(5,3)
2x + y = 13
2(5) + y = 13
10 + y = 13
y=3
Practice
Solve using substitution.
1) x – 2y = 8
2x + y = 8
2) 3x + 4y = 2
2x – y = 5
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
x=y+4
y + 4 + 2y = 13
3y + 4 = 13
3y = 9
y=3
x=y+4
x=3+4
x=7
Practice
Translate to a system of equations and solve.
1) The sum of two numbers is 84. One number
is three times the other. Find the numbers.