SISTEMA DE EQUAÇÕES do 1º grau | Método da SUBSTITUIÇÃO | Matemática Básica \Prof. Gis/

Summary

In this lesson, Gis introduces the concept of solving first-degree equation systems, focusing on the substitution method. Through a practical example involving a snack bar's promotional offers, Gis teaches how to represent a real-life situation with equations and solve for unknowns. The lesson covers the process of setting up equations with two unknowns, isolating variables, and substituting to find solutions. Gis also provides a second example about animals in a backyard, reinforcing the use of substitution. Viewers are encouraged to follow along and practice the method in future lessons. The video concludes with a reminder to subscribe and engage with the channel.

Takeaways

• 😀 The substitution method is one of the four main techniques for solving systems of first-degree equations.
• 😀 In the substitution method, you isolate one variable in an equation and substitute it into another equation to solve for the variables.
• 😀 The script explains a real-life example of using a system of equations to solve a snack bar promotion problem with cheese bread and coffee prices.
• 😀 The substitution method involves isolating one unknown (e.g., X for cheese bread) and then substituting it into the other equation to solve for the second unknown (e.g., Y for coffee).
• 😀 The problem of finding the price of cheese bread and coffee was solved step by step, with final answers: cheese bread costs 2 reais and coffee costs 1 real.
• 😀 The second example in the script used a real-life scenario involving dogs and chickens in a backyard, with the goal of finding how many of each animal there are based on the total number of heads and feet.
• 😀 The system of equations for the backyard problem was translated into two equations with unknowns for the number of dogs (C) and chickens (G).
• 😀 The solution to the backyard problem involved solving the system of equations using the substitution method, resulting in 5 chickens and 3 dogs.
• 😀 The script emphasizes that a system of equations is made up of two equations and two unknowns, and each equation depends on the other to find a solution.
• 😀 The instructor encourages students to practice by transcribing word problems into system equations and solving them using the substitution method.
• 😀 At the end of the lesson, viewers are invited to subscribe, like the video, and look forward to the next class on the addition method for solving systems of equations.

Q & A

What is the first degree equation system covered in the class?

The first degree equation system involves solving systems of equations that contain two unknowns. In this class, the system is solved using the substitution method.

What are the four methods to solve a first degree equation system?

The four methods to solve a first degree equation system are: Addition method, Comparison method, Substitution method, and the Geometric method.

Why did the instructor use a snack bar promotion as an example?

The instructor used a snack bar promotion as an example to demonstrate how to create a system of equations with two unknowns, such as the cost of cheese bread and coffee.

What are the unknowns in the problem involving the snack bar promotion?

In the snack bar promotion problem, the unknowns are the cost of the cheese bread (denoted as 'x') and the cost of the coffee (denoted as 'y').

How did the instructor write the system of equations for the snack bar example?

The system of equations for the snack bar problem is written as: 2x + y = 5 (for two cheese breads and one coffee) and x + 2y = 4 (for one cheese bread and two coffees).

What is the first step in solving the system using the substitution method?

The first step in solving the system using the substitution method is to isolate one of the unknowns. In this case, the instructor isolated 'x' from the second equation.

How do you solve for 'x' in the equation x + 2y = 4?

To solve for 'x', the equation is rearranged to x = 4 - 2y. This isolates 'x' on one side of the equation.

What does the substitution method involve after isolating an unknown?

After isolating an unknown, the next step in the substitution method is to substitute the expression for the isolated variable into the other equation to solve for the remaining unknown.

How did the instructor solve for the cost of each item in the snack bar example?

The instructor substituted the expression for 'x' (4 - 2y) into the first equation, simplified, and solved for 'y', finding that each coffee costs 1 real. Then, by substituting this value of 'y' back, the instructor determined that each cheese bread costs 2 reais.

How does the instructor solve the second example involving chickens and dogs?

In the second example, the instructor defines two unknowns: 'c' for chickens and 'g' for dogs. The system of equations is then written as: c + g = 8 (total heads) and 4c + 2g = 22 (total feet). The substitution method is used to solve this system, ultimately finding there are 5 chickens and 3 dogs.