Transcript Solving Systems of Equations using Substitution

Name:
Date:
Period:
Topic: 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:
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 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?
Name:
Date:
Period:
Topic: 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:
Find the solution to the following system of equations by GRAPHING:
y = 2x + 2
2x + 4y = 8
Period 1, 5
Home-Learning #6 Review:
GIVEN EXAMPLE:
y= 4x
3x+y=-21
STEP1:
y=4x (Already solved for y)
STEP 2:
Substitute into second equation:
3x + y = -21 becomes:
GIVEN EXAMPLE:
y= 4x
3x+y=-21
STEP 3: Solve for the variable
3x + y = -21 becomes 3x + 4x = - 21
GIVEN EXAMPLE:
y= 4x
3x+y=-21
STEP 4: Solve for the other
variable use x=-3 and y=4x
y = 4x
3x + y = -21
Step 5: Check the solution in both equations.
Solution to the system is (-3,-12).
y = 4x
-12 = 4(-3)
-12 = -12
3x + y = -21
3(-3) + (-12) = -21
-9 + (-12) = -21
-21= -21
Solving a system of equations by
substitution
Step 1: Solve an equation for
one variable.
Pick the easier equation. The goal
is to get y= ; x= ; a= ; etc.
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.
Step 5: Check your
solution.
Substitute the value of the variable
into the equation.
Substitute your ordered pair into
BOTH equations.
Solve the system using substitution
x+y=5
y=3+x
Step 1: Solve an equation
for one variable.
Step 2: Substitute
Step 3: Solve the
equation.
The second equation is
already solved for y!
x+y=5
x + (3 + x) = 5
2x + 3 = 5
2x = 2
x=1
Solve the system using substitution
x+y=5
y=3+x
Step 4: Plug back in to find
the other variable.
Step 5: Check your
solution.
x+y=5
(1) + y = 5
y=4
(1, 4)
(1) + (4) = 5
(4) = 3 + (1)
The solution is (1, 4). What do you think the answer would
be if you graphed the two equations?
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.
x + y = 10
5x – y = 2
Step 3: Simplify and solve the equation.
x + y = 10
5x – y = 2
Step 4: Substitute back into either original
equation to find the value of the other
variable.
x + y = 10
5x – y = 2
Step 5: Check the solution in both equations.
Solution to the system is (2, 8).
Solve by substitution:
y  2x  2
2x  3y  10
Your Turn!
Which answer checks correctly?
3x – y = 4
x = 4y - 17
1.
2.
3.
4.
(2, 2)
(5, 3)
(3, 5)
(3, -5)
Additional Practice:
Page 371 (1 – 4)
Activity: Puzzle
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)