Podcast
Questions and Answers
What are the two numbers if the sum is 24 and their difference is 16?
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?
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?
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?
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?
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?
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?
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?
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?
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?
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.
