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Summary

In this video, the presenter explains how to solve a system of linear equations to determine the weight of three types of balls: basketball, soccer ball, and volleyball. The process involves defining variables for each ball, translating the problem into equations, and using methods like elimination and substitution to solve for the unknowns. The solution reveals the weight of the basketball as 650 grams, the soccer ball as 450 grams, and the volleyball as 250 grams. The video provides a clear, step-by-step approach to solving systems of equations in a practical context.

Takeaways

• 😀 The script focuses on solving a system of linear equations to determine the weight of three types of balls: basketball, soccer ball, and volleyball.
• 😀 The variables are defined as follows: X for basketball, Y for soccer ball, and Z for volleyball.
• 😀 The problem provides three conditions, each leading to a mathematical equation involving the weights of the balls.
• 😀 The first equation is: 2X + Y + 3Z = 2500, representing the weight of two basketballs, one soccer ball, and three volleyballs.
• 😀 The second equation is: X + 2Y + 2Z = 2500, which corresponds to one basketball, two soccer balls, and two volleyballs.
• 😀 The third equation is: 2X + Z = 1550, involving two basketballs and one volleyball.
• 😀 The system of equations is solved using a combination of elimination and substitution methods.
• 😀 By eliminating variable Y, the script simplifies the equations into new ones to help solve for X, Y, and Z.
• 😀 Through substitution, the script determines that X (basketball) = 650, Y (soccer ball) = 450, and Z (volleyball) = 250.
• 😀 The final results give the individual weights of each ball: basketball = 650 grams, soccer ball = 450 grams, and volleyball = 250 grams.
• 😀 The script emphasizes the importance of correctly interpreting the equations and using systematic methods like substitution and elimination to solve the system.

Q & A

What are the variables used to represent the weight of each type of ball in the problem?

The variables used are X for the weight of the basketball, Y for the weight of the soccer ball, and Z for the weight of the volleyball.

What is the first equation derived from the given information?

The first equation is 2X + Y + 3Z = 2500, which represents the weight of two basketballs, one soccer ball, and three volleyballs.

What is the second equation based on the second weighing?

The second equation is X + 2Y + 2Z = 2050, which represents the weight of one basketball, two soccer balls, and two volleyballs.

What is the third equation from the third weighing?

The third equation is 2X + Z = 1550, representing the weight of two basketballs and one volleyball.

What method is used to solve the system of equations?

The method used to solve the system is a combination of elimination and substitution.

How is the variable Y eliminated from the equations?

To eliminate Y, the first equation is multiplied by 2, and then the second equation is subtracted from it to eliminate the Y terms.

After eliminating Y, what is the resulting equation?

The resulting equation after eliminating Y is 3X + 4Z = 2950.

How is the variable Z eliminated next?

To eliminate Z, the third equation is multiplied by 4, and then the resulting equation is subtracted from the fourth equation.

What is the value of X after solving the equations?

The value of X, representing the weight of the basketball, is 650 grams.

How are the values of Y and Z determined after finding X?

The values of Y and Z are found by substituting X into the first equation to solve for Y, and using the second equation to solve for Z. The final values are Y = 450 grams (soccer ball) and Z = 250 grams (volleyball).