Solving Linear Equations and Word Problems

The video tutorial introduces the topic of solving word problems using systems of linear equations with three variables, aimed at 10th-grade mathematics students. It outlines a four-step process: defining variables, creating mathematical models, solving the equations, and interpreting the results. The tutorial uses a fruit purchase scenario to demonstrate the process, employing elimination and substitution methods. The video concludes with practice problems for students to apply the learned concepts.

What is the first step in solving word problems involving linear equations in three variables?

• Solve the equations

• Make assumptions

• Interpret the results

• Model the equations

In the example problem, how many kilograms of oranges did Amel buy?

• 1 kg

• 3 kg

• 4 kg

• 2 kg

Which method can be used to solve the system of equations in the example problem?

• Factoring

• Matrix

• Substitution

• Graphing

What is the equation formed from Freya's purchase?

• 3x + 2z = 79000

• x + y + z = 100000

• 2x + y + 4z = 112000

• 2y + z = 58000

What is the result of eliminating y from the first two equations?

• 3x + 2z = 79000

• 2x + y + 4z = 112000

• 4x + 8z = 224000

• 4x + 7z = 166000

What is the value of z after solving the equations?

• 14000

• 17000

• 22000

• 58000

What is the value of x after substituting z?

• 58000

• 14000

• 17000

• 22000

What is the value of y after substituting z?

• 22000

• 58000

• 17000

• 14000

Which fruit was the most expensive in the example problem?

• Oranges

• Apples

• Bananas

• Grapes

If Green buys 2 notebooks, 1 pencil, and 1 pen, how much does he need to pay?

• 5700

• 10700

• 6700

• 8200