Lesson Twelve
WORD PROBLEMS USING SYSTEMS OF
EQUATIONS
SOLVING WORD PROBLEMS
Steps in solving word problems using systems
of equations
 1. Represent unknown quantities into two
different variables
 2. Use relationship given in the problem to setup the system of equations
 3. Solve for the unknown variables
 4. Give the answer
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NUMBER PROBLEM
Ex. The sum of two numbers is 30. The
difference of these two numbers is 6. Find the
two numbers.
 Let x be the first number
 y be the second number
 System of equations are
𝑥 + 𝑦 = 30
𝑥−𝑦 =6

NUMBER PROBLEM
Solve x and y using elimination
𝑥 + 𝑦 = 30

+
𝑥−𝑦 =6
2𝑥 = 36
𝑥 = 18
18 − 𝑦 = 12
𝑦 = 12
 The two numbers are 12 and 18.
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GEOMETRY PROBLEMS
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Ex. The perimeter of a rectangle is 70 m. Its length is 5
more than twice its width. What is the width of the
rectangle?
Let x = be the width of the rectangle
y = be the length of the rectangle
System of equation
“length is 5 more than its width”
𝑦 = 5 + 2𝑥
“perimeter is 70 m”
2 𝑥 + 𝑦 = 70
GEOMETRY PROBLEMS
Solve the system of equation
−2𝑥 + 𝑦 = 5
2𝑥 + 2𝑦 = 70
 Solve by elimination
3𝑦 = 75
𝑦 = 25
2𝑥 + 2 25 = 70
2𝑥 + 50 = 70
2𝑥 = 20
𝑥 = 10
The width of the rectangle is 10m
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INVESTMENT PROBLEMS
Mrs. Castro deposited a total of Php 220 000 in
two different banks. One bank paid 5 % and the
other paid 6 %. In one year the total interest was
Php 12000. What is the amount invested at 5%?
 Let x = be the amount invested at 5%
 y = be the amount invested at 6%
 “deposited a total of Php 220000”
 𝑥 + 𝑦 = 220000
 “total interest was 12000”
 0.05𝑥 + 0.06𝑦 = 12000
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INVESTMENT PROBLEMS
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Solve the system of equation
Multiply by -0.06
−0.06 𝑥 + 𝑦 = −0.06 220000
0.05𝑥 + 0.06𝑦 = 12000
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−0.06𝑥 − 0.06𝑦 = −13200
0.05𝑥 + 0.06𝑦 = 12000
−0.01𝑥 = −1200
𝑥 = 120 000
The amount deposited is Php 120 000.
AGE PROBLEMS
Ex. Kathy is 8 years older than Jane. In seven
years, Kathy will be twice as old as Jane. How old
is Kathy?
 Let x be the present age of Jane
 y be the present age of Kathy
 x + 7 is the age of Jane in 7 years
 y+ 7 is the age of Kathy in 7 years
 System of equation
𝑦 =𝑥+8
𝑦 + 7 = 2(𝑥 + 7)
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AGE PROBLEMS
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Solve the system of equation
𝑦 + 7 = 2(𝑥 + 7)
𝑦 + 7 = 2𝑥 + 14

−𝑥 + 𝑦 = 8
−2𝑥 + 𝑦 = 7
2𝑥 − 2𝑦 = −16
−2𝑥 + 𝑦 = 7
−𝑦 = −9
𝑦=9

Kathy is 9 years old.