Transcript Lesson 3

Lesson 7-3
Elimination Using
Addition and Subtraction
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Objectives
• Solve system of equations by using
elimination with addition
• Solve system of equations by using
elimination with subtraction
Vocabulary
• Elimination - the use of addition or subtraction to
eliminate one variable and solve a system of
equations
Solve Systems of Equations: Elimination
• Sometimes we can add (or subtract) two sets of
equations together and eliminate a variable
• We can do this because we are adding (or subtracting)
the same thing (since they are equal) from both sides
of the equation
• Example: Solve 2x + 3y = 23 and -2x + 8y = 32
2x + 3y = 23
+ -2x + 8y = 32
11y = 55
y=5
2x + 3(5) = 23
2x = 8
x=4
(equation one)
(equation two)
Eliminate x by adding
Divide both sides by 11
Sub y= into equation one
Simplifying
Divide both sides by 3
Example 1
Use elimination to solve the system of equations.
Since the coefficients of the x terms, –3 and 3, are
additive inverses, you can eliminate the x terms by
adding the equations.
Write the equation in column
form and add.
Notice that the x value is eliminated.
Divide each side by –2.
Simplify.
Example 1 cont
Now substitute –15 for y in either equation to find the
value of x.
First equation
Replace y with –15.
Simplify.
Add 60 to each side.
Simplify.
Divide each side by –3.
Simplify.
Answer: The solution is (–24, –15).
Example 2
Four times one number minus three times another
number is 12. Two times the first number added to
three times the second number is 6. Find the numbers.
Let x represent the first number and y represent the
second number.
Four times
one number
4x
Two times
the first number
2x
minus
three times
another number
is
12.
–
3y
=
12
added to
three times
the second number
is
6.
+
3y
=
6
Example 2 cont
Use elimination to solve the system.
Write the equation in column
form and add.
Notice that the y value is eliminated.
Divide each side by 6.
Simplify.
Example 2 cont
Now substitute 3 for x in either equation to find the value of y.
First equation
Replace x with 3.
Simplify.
Subtract 12 from each side.
Simplify.
Divide each side by –3.
Simplify.
Answer: The numbers are 3 and 0.
Example 3
Use elimination to solve the system of equations.
Since the coefficients of the x terms, 4 and 4, are the same,
you can eliminate the x terms by subtracting the equations.
Write the equation in column
form and subtract.
Notice that the x value is eliminated.
Divide each side by 5.
Simplify.
Example 3 cont
Now substitute 2 for y in either equation to find the
value of x.
Second equation
Simplify.
Add 6 to each side.
Simplify.
Divide each side by 4.
Simplify.
Answer: The solution is (6, 2).
Summary & Homework
• Summary:
– Sometimes adding or subtracting two equations
will eliminate one variable
• Homework:
– Pg 385 12-24 even, 30, 32