Questions and Answers
What are the two numbers if the sum is 24 and their difference is 16?
20 and 4
How many Gr. 7 and Gr. 8 students attended the Math Fair if the total number of students is 340 and the total collected amount is Php 3,040?
180 Gr. 7 students and 160 Gr. 8 students
What is the daily wage of a washing machine operator and a supervisor if 6 operators and 2 supervisors earn Php 2,720 and promoting one operator increases it to Php 2,800?
Php 320 for a washing machine operator and Php 400 for a supervisor
What are the dimensions of a rectangular lot with a perimeter of 420 meters and the width being 120 meters less than its length?
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How old are Jessie and Jade if Jessie is 4 times as old as Jade, and in 10 years Jessie will be thrice as old as Jade?
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What is the two-digit number if the sum of its digits is 9 and the tens digit is three more than the units digit?
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How long does Cherry spend in running if she trains for 4 hours, running at 6 miles per hour and walking back at 2 miles per hour?
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What are the two numbers if the sum is 16 and their difference is 2?
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What is Sam's present age if the sum of the ages of Sam and Cath is 40 years and in 10 years, Sam will be twice as old as Cath?
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What are the measures of two complementary angles if one angle is twice the other?
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Study Notes
Solving Problems Involving Linear Equations
- The elimination method is used to solve systems of linear equations by removing one variable to find the solution.
Example Problems
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Problem 1:
- Two numbers sum to 24, and their difference is 16.
- Let x be the first number and y be the second.
- Solution yields x = 20 and y = 4.
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Problem 2:
- Alicia High School Math Fair: Php 8 admission for Grade 7 and Php 10 for Grade 8.
- Total of 340 students attended, generating Php 3,040.
- Solution: 180 Grade 7 students and 160 Grade 8 students attended.
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Problem 3:
- A laundry shop employs 6 operators and 2 supervisors, incurring Php 2,720 in wages.
- If one operator becomes a supervisor, new total wage is Php 2,800.
- Solution yields a machine operator wage of Php 320 and supervisor wage of Php 400.
Additional Problems with Substitution Method
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Problem 4:
- A rectangular lot's perimeter is 420 meters, and the width is 120 meters less than the length.
- Dimensions can be evaluated using the substitution method.
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Jessie and Jade's Ages:
- Jessie is four times Jade's age; in 10 years, Jessie will be three times Jade's age.
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Two-Digit Number:
- The sum of the digits is 9, with the tens digit being three more than the unit digit.
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Cherry's Training:
- Runs at 6 mph for part of training and walks back at 2 mph over 4 hours.
Graphical Method Problems
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Two Numbers:
- The sum of two numbers is 16, and their difference is 2; solution gives numbers 9 and 7.
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Ages of Sam and Cath:
- Their ages sum to 40 years. After 10 years, Sam will be twice as old as Cath.
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Complementary Angles:
- Two angles add up to 90 degrees; one angle is twice the other.
Summary
- Understanding elimination and substitution methods is crucial for solving systems of linear equations efficiently.
- Practical applications include real-world scenarios such as financial contributions, wages, and geometric problems.
Studying That Suits You
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Description
This quiz focuses on solving systems of linear equations using elimination, substitution, and graphical methods. Designed for Grade 8 students, it challenges learners to apply these techniques to find solutions for given problems. Test your understanding of these essential algebraic concepts.
