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Elimination Using Addition and Subtraction. Math Pacing. The sum of two numbers is 31. The greater number is 5 more than the lesser number. What are the two numbers? - PowerPoint PPT PresentationTRANSCRIPT
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Elimination Using Addition and Subtraction
1. The sum of two numbers is 31. The greater number is 5 more than the lesser number. What are the two numbers?
2. Complementary angles have a sum of 90°. Angles A and B are complementary and the measure of angle A is 14 ° less than the measure of angle B. Find the measures of angles A and B.
3. What value of c in the system of equations 5x + y = – 1 and – 2y = 10x + c will produce a system of equations with infinitely many solutions?
Let x = the greater numberLet y = the lesser number 5
31
yx
yx 315 yy262 y
13y
18x
Let x = the measure of ALet y = the measure of B 14
90
yx
yx 9014 yy1042 y
52y
38x
15 yx 15 xy 2102 xy 2c
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Elimination Using Addition and Subtraction
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Elimination Using Addition and Subtraction
Sometimes adding two equations together will eliminate one variable.
Using this step to solve a system of equations is called elimination.
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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.
Elimination Using Addition
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Now substitute –15 for y in either equation to find the value of x.
Simplify.
Add 60 to each side.
Divide each side by –3.
Simplify.
First equation
Replace y with –15.
Simplify.
Answer: The solution is (–24, –15).
Elimination Using Addition
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Use elimination to solve the system of equations.
Answer: (2, 1)
Elimination Using Addition
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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 minus
three times another number is 12.
Two times the first number added to
three times the second number is 6.
4x – 3y = 12
2x + 3y = 6
Write and Solve a System of Equations
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Use elimination to solve the system.
Notice that the y value is eliminated.
Divide each side by 6.
Simplify.
Write the equation in column form and add.
Write and Solve a System of Equations
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Now substitute 3 for x in either equation to find the value of y.
Answer: The numbers are 3 and 0.
First equation
Replace x with 3.
Simplify.
Subtract 12 from each side.
Simplify.
Divide each side by –3.
Simplify.
Write and Solve a System of Equations
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Four times one number added to another number is –10. Three times the first number minus the second number is –11. Find the numbers.
Answer: –3, 2
Write and Solve a System of Equations
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Elimination Using Addition and Subtraction
Sometimes subtracting one equation from another will eliminate one variable.
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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.
Elimination Using SubtractionUse elimination to solve the system of equations.
–
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Now substitute 2 for y in either equation to find the value of x.
Answer: The solution is (6, 2).
Second equation
Simplify.
Add 6 to each side.
Simplify.
Divide each side by 4.
Simplify.
Elimination Using Subtraction
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Use elimination to solve the system of equations.
Answer: The solution is (2, –6).
Elimination Using Subtraction
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Multiple-Choice Test Item
If and what is the value of y?A (3, –8) B 3 C –8 D (–8, 3)
Read the Test ItemYou are given a system of equations, and you are
asked to find the value of y.
Elimination Using Subtraction
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Solve the Test ItemYou can eliminate the y terms by subtracting one equation from the other.
Write the equation in column form and subtract.
Notice that the y value is eliminated.
Divide each side by 14.
Simplify.
Elimination Using Subtraction
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Now substitute 3 for x in either equation to solve for y.
Answer: C
Notice that B is the value of x and A is the solution of the system of equations. However, the question asks for the value of y.
First equation
Simplify.
Subtract 24 from each side.
Simplify.
Elimination Using Subtraction
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Multiple-Choice Test Item
If and what is the value of x?A 4 B (4, –4) C (–4, 4) D –4
Answer: D
Elimination Using Subtraction