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

Summary

In this engaging lesson, Gis explains how to solve systems of first-degree equations using the addition method, building on her previous substitution method tutorial. She introduces a real-life problem involving the ages of two sisters, Gis and Karina, showing how to apply the method step by step to find their ages. Gis emphasizes that while the addition method is useful, the substitution method may be better for solving second-degree equations. The lesson includes multiple examples to help students understand when and how to apply the method for different types of systems, along with a call to subscribe to her channel for more educational content.

Takeaways

• 😀 Gis introduces the addition method for solving systems of equations, focusing on how it can be applied to real-life situations like calculating the ages of people.
• 😀 The instructor emphasizes the importance of subscribing to the channel, sharing the video, and engaging with the content, encouraging a supportive learning community.
• 😀 Gis explains how to translate a word problem into a system of equations and solve it using algebraic methods like addition and subtraction.
• 😀 The age-related word problem involves the sum and difference of Gis and her sister Karina's ages, resulting in two equations that need to be solved together.
• 😀 Gis walks through solving the system of equations step-by-step, first adding the equations to eliminate one variable, and then solving for the remaining variable.
• 😀 The addition method simplifies the system by eliminating one unknown, making it easier to solve the system of equations and find the values of the variables.
• 😀 Gis highlights that while the addition method works well in certain cases, the substitution method might be more efficient for other types of systems, particularly quadratic equations.
• 😀 In the second example, Gis explains how to use the addition method to zero out a variable (y) by multiplying one equation by a constant to make the coefficients of y opposites.
• 😀 The solution set is presented as an ordered pair of values for x and y, showing how the solution to the system can be expressed clearly.
• 😀 Gis provides further examples, demonstrating that finding the least common multiple (LCM) is key when choosing the right number to multiply equations for elimination.

Q & A

What is the key difference between the substitution and addition methods in solving systems of equations?

The substitution method involves solving one equation for one variable and substituting it into the other equation. The addition method, on the other hand, involves adding or subtracting the equations to eliminate one variable, making it easier to solve for the other.

Why is it important to choose the correct method when solving systems of equations?

Choosing the correct method depends on the system's structure. The addition method is useful when the coefficients of one variable are opposites, making it easy to eliminate that variable. The substitution method is ideal when one variable is easily isolated. Using the right method simplifies the solution process.

How does the addition method help in solving systems of equations?

The addition method works by combining the equations to eliminate one variable. After adding or subtracting the equations, the remaining equation with only one variable can be solved directly.

What happens when you add two equations where the variables have the same sign?

When the variables have the same sign, adding the equations does not eliminate them. In such cases, the addition method won't work unless you manipulate the coefficients by multiplying the equations to make one variable's coefficient the opposite of the other.

What does the term 'MMC' refer to in solving systems of equations?

MMC stands for 'Mínimo Múltiplo Comum' (Least Common Multiple). It is used to find a common multiple of the coefficients of variables in the equations, making it possible to eliminate one of the variables by multiplying the equations accordingly.

How did Gis demonstrate solving a system with the ages of herself and her sister Karina?

Gis demonstrated solving the system by translating the problem into two equations: the sum of their ages equaling 48 and the difference between their ages being 8. Using the addition method, she eliminated one variable and found Gis' age to be 28 and Karina's age to be 20.

What was the issue when Gis tried to solve a system with an equation that didn’t immediately lead to a zeroed variable?

Gis encountered a situation where the addition method didn’t immediately eliminate a variable. To solve this, she used the Least Common Multiple (MMC) to adjust the coefficients of the variables so that one of the variables would cancel out when the equations were added.

Why is it not always straightforward to solve systems using the addition method?

It’s not always straightforward because not all systems have coefficients that directly cancel out when added. In such cases, it’s necessary to multiply the equations to adjust the coefficients before the addition method can successfully eliminate a variable.

In the context of Gis’ explanation, how do you handle a system that is not contextualized?

For non-contextualized systems, the solution is given as a set of ordered pairs, where each pair represents the values of the variables that satisfy the system. For example, an ordered pair (x, y) represents the solution to the system of equations.

What did Gis say about the usefulness of the substitution method in systems of second-degree equations?

Gis mentioned that the substitution method is often more useful for solving systems of second-degree equations, as these systems tend to be more complex and require isolating one variable to simplify the solution process.