A man wanted to get into his work building, but he had forgotten his code. However, he did remember five clues. These are what those clues were: The fifth number plus the third number equals fourteen. The fourth number is one more than the second

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A man wanted to get into his work building, but
he had forgotten his code. However, he did
remember five clues. These are what those clues
wereThe fifth number plus the third number
equals fourteen. The fourth number is one more
than the second number. The first number is one
less than twice the second number. The second
number plus the third number equals ten. The
sum of all five numbers is 30.What were the
five numbers and in what order?
NameDatePeriodTopic Solving Systems of
Equations by Substitution Essential Question
When is using substitution a better option to
find a solution to systems of equations?
Warm-Up
2
Find the solution to the following system of
equations by GRAPHINGy 2x 22x 4y 8
NameDatePeriodTopic Solving Systems of
Equations by Substitution Essential Question
When is using substitution a better option to
find a solution to systems of equations?
Warm-Up
Period 1, 5
3
Home-Learning 6 Review
4
GIVEN EXAMPLE
y 4x 3xy-21
STEP1 y4x (Already solved for y)
STEP 2 Substitute into second equation 3x
y -21 becomes
5
GIVEN EXAMPLE
y 4x 3xy-21
STEP 3 Solve for the variable 3x y -21
becomes 3x 4x - 21
6
GIVEN EXAMPLE
y 4x 3xy-21
STEP 4 Solve for the other variable use x-3 and
y4x
7

y 4x 3x y -21
Step 5 Check the solution in both equations.
Solution to the system is (-3,-12).
3x y -21 3(-3) (-12) -21 -9
(-12) -21 -21 -21
y 4x -12 4(-3) -12 -12
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Solving a system of equations by
substitution
Pick the easier equation. The goal is to get y
x a etc.

• Step 1 Solve an equation for one variable.

Step 2 Substitute
Put the equation solved in Step 1 into the other
equation.
Step 3 Solve the equation.
Get the variable by itself.
Step 4 Plug back in to find the other variable.
Substitute the value of the variable into the
equation.
Step 5 Check your solution.
Substitute your ordered pair into BOTH equations.
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Solve the system using substitution

• x y 5
• y 3 x

Step 1 Solve an equation for one variable.
The second equation is already solved for y!
Step 2 Substitute
x y 5x (3 x) 5
2x 3 5 2x 2 x 1
Step 3 Solve the equation.
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Solve the system using substitution

• x y 5
• y 3 x

x y 5 (1) y 5 y 4
Step 4 Plug back in to find the other variable.
(1, 4) (1) (4) 5 (4) 3 (1)
Step 5 Check your solution.
The solution is (1, 4). What do you think the
answer would be if you graphed the two equations?
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What about this one?
x y 10 5x y 2
Step 1 Solve one equation for one variable.
Step 2 Substitute the expression from step one
into the other equation.
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x y 10 5x y 2
Step 3 Simplify and solve the equation.
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x y 10 5x y 2
Step 4 Substitute back into either original
equation to find the value of the
other variable.
14

x y 10 5x y 2
Step 5 Check the solution in both equations.
Solution to the system is (2, 8).
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Solve by substitution
Your Turn!

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Which answer checks correctly?
3x y 4 x 4y - 17

1. (2, 2)
2. (5, 3)
3. (3, 5)
4. (3, -5)

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Additional Practice

• Page 371 (1 4)

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Activity Puzzle
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Wrap-Up

• Determine what problems from previous class could
  you easily solve by utilizing the substitution
  strategy
• Vocabulary Review
• Summary

• Home-Learning 7
• Page 371 373 (12, 17, 28, 35, 44)