Solving Problems Involving Linear Equations PDF
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Alicia National High School
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Summary
This document provides examples of solving problems involving linear equations using elimination, substitution, and graphing methods. The problems are presented step-by-step for better understanding. Topics presented include finding two numbers from sum and difference, solving for the number of students for a fundraiser, wages of workers within a business, determining dimensions of a rectangular lot, finding ages, and finding angles.
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SOLVING PROBLEMS INVOLVING SYSTEMS OF LINEAR EQUATIONS BY ELIMINATION, SUBSTITUTION, and GRAPHICAL METHOD GRADE 8 INTERMEDIATE ALGEBRA Solve using ELIMINATION METHOD 1. The sum of two numbers is 24 and their difference is 16. Find the two numbers. Solve using ELIMINATION METHOD...
SOLVING PROBLEMS INVOLVING SYSTEMS OF LINEAR EQUATIONS BY ELIMINATION, SUBSTITUTION, and GRAPHICAL METHOD GRADE 8 INTERMEDIATE ALGEBRA Solve using ELIMINATION METHOD 1. The sum of two numbers is 24 and their difference is 16. Find the two numbers. Solve using ELIMINATION METHOD 1. The sum of two numbers is 24 and their difference is 16. Find the two numbers. Let x be the 1st number and y be the 2nd number Solve using ELIMINATION METHOD 1. The sum of two numbers is 24 and their difference is 16. Find the two numbers. Let x be the 1st number and y be the 2nd number Therefore, the two numbers are 20 and 4. Solve using ELIMINATION METHOD Problem 2. Math club of Alicia High School held a Math Fair for Gr. 7 and Gr. 8 students last year. The admission at the fair is Php 8 for Gr. 7 participants and Php 10 for Gr.8 participants. On that fair, a total of 340 students are present and math club collected a total amount of Php 3,040. How many Gr.7 and Gr. 8 students attended the fair? Math club of Alicia High School held a Math Fair for Gr. 7 and Gr. 8 students last year. The admission at the fair is Php 8 for Gr. 7 participants and Php 10 for Gr.8 participants. On that fair, a total of 340 students are present and math club collected a total amount of Php 3,040. How many Gr.7 and Gr. 8 students attended the fair? Substitute the value of x in any of the original equations, then solve for y. Therefore, there were 180 Gr.7 students and 160 Gr. 8 students attended the fair. Solve using ELIMINATION METHOD Problem 3. A Laundry shop hires 6 washing machine operator assistant and 2 supervisors for total daily wages of Php 2,720. If one of the machine operators is promoted to a supervisor, the total daily wages become Php 2,800. What is the daily wage of a machine operator and a supervisor? A Laundry shop hires 6 washing machine operator assistant and 2 supervisors for total daily wages of Php 2,720. If one of the machine operators is promoted to a supervisor, the total daily wages become Php 2,800. What is the daily wage of a machine operator and a supervisor? Substitute the value of x in any of the original equation to get the value of y Multiply the 1st equation by 3 and the 2nd equation by -2, then add the two equations. Therefore, the daily wage of washing machine operator is Php 320 and the daily wage of a supervisor is Php 400. Solve using SUBSTITUTION METHOD Problem 4. A rectangular lot in Barangay Pinagbuhatan has a perimeter of 420 meters. The width of the lot is 120 meters less than its length. Find the dimensions. A rectangular lot in Barangay Pinagbuhatan has a perimeter of 420 meters. The width of the lot is 120 meters less than its length. Find the dimensions. A rectangular lot in Barangay Pinagbuhatan has a perimeter of 420 meters. The width of the lot is 120 meters less than its length. Find the dimensions. A rectangular lot in Barangay Pinagbuhatan has a perimeter of 420 meters. The width of the lot is 120 meters less than its length. Find the dimensions. A rectangular lot in Barangay Pinagbuhatan has a perimeter of 420 meters. The width of the lot is 120 meters less than its length. Find the dimensions. If Jessie is 4 times as old as Jade, and 10 years from now Jessie will be thrice as old as Jade. How old is Jessie and Jade? If Jessie is 4 times as old as Jade, and 10 years from now Jessie will be thrice as old as Jade. How old is Jessie and Jade? If Jessie is 4 times as old as Jade, and 10 years from now Jessie will be thrice as old as Jade. How old is Jessie and Jade? The sum of the digits of a two-digit number is 9. The tens digit is three more than the unit digit. Find the number. Cherry spends 4 hours training for the upcoming race competition at Rizal High School. She runs full speed at 6 miles per hour, then she walks back to her starting point at 2 miles per hour. How long does she spend in running? and How long does she spend in walking? Graphical method The sum of two numbers is 16 and their difference is 2. Find the two numbers. The sum of two numbers is 16 and their difference is 2. Find the two numbers. Therefore, the two numbers are 9 and 7. Graphical method The sum of the ages of Sam and Cath is 40 years. After 10 years, Sam will be twice as old as Cath. What is Sam’s present age? What is Cat’s present age? Graphical method Two angles are complementary. One angle is twice the other. Find the two angles.
