PERSAMAAN LINEAR DUA VARIABEL (PLDV) KELAS 9

Summary

In this educational video, the Sigma Smart Study learning channel introduces the concept of linear equations in two variables for grade 9 students. It explains the key components of a linear equation, including the requirements for two variables and the power of the variables. The video demonstrates various methods to solve these equations, including substitution, elimination, and graphical methods, through step-by-step examples. By the end, viewers will have a clear understanding of how to approach and solve linear equations, helping students grasp the fundamental concepts of algebra.

Takeaways

• 😀 A linear equation in two variables has two variables, typically represented by x and y, and each variable is raised to the power of 1.
• 😀 For an equation to be classified as a linear equation in two variables, it must not contain powers greater than 1 or involve multiplication between variables (e.g., no x^2 or xy).
• 😀 An example of a linear equation in two variables is 2x + 3y = 6, where x and y are the variables and 2, 3, and 6 are the constants.
• 😀 The general form of a linear equation in two variables is ax + by = c, where a and b are coefficients, x and y are variables, and c is a constant.
• 😀 Three main methods for solving systems of linear equations are: substitution, elimination, and graphical methods.
• 😀 The substitution method involves solving one equation for one variable and then substituting that value into the other equation to find the remaining variable.
• 😀 An example of the substitution method is solving x = y + 3 and x + y = 11, where substitution leads to the solution y = 4 and x = 7.
• 😀 The elimination method involves adding or subtracting equations to eliminate one variable, then solving for the remaining variable.
• 😀 An example of the elimination method is using the equations x + y = 10 and x - y = 4 to eliminate y and solve for x = 7, then using the value of x to solve for y = 3.
• 😀 The graphical method involves plotting the equations on a coordinate plane and finding the point of intersection, which represents the solution to the system of equations.
• 😀 An example of the graphical method shows how to plot two equations, x + y = 8 and x - y = 2, and find their intersection at the point (5, 3).

Q & A

What is a linear equation in two variables?

A linear equation in two variables is an equation that has two variables, typically represented as x and y, where each variable is raised to the power of 1. The equation cannot have variables raised to a power greater than 1 or involve multiplication between variables.

What are the conditions for an equation to be a linear equation in two variables?

For an equation to be a linear equation in two variables, it must meet two conditions: 1) It must have two different variables (usually x and y). 2) Each variable must have a power of 1, with no terms like x^2, x^3, or xy.

Which of the following is a linear equation in two variables: 2x + 3 = 7, x^2 + y = 9, 3x + 2y = 12, or x + y + z = 10?

The correct answer is '3x + 2y = 12' because it involves two variables (x and y), and neither of them has a power greater than 1.

What is the general form of a linear equation in two variables?

The general form of a linear equation in two variables is ax + by = c, where a and b are the coefficients, x and y are the variables, and c is a constant.

What is the substitution method for solving linear equations in two variables?

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to solve for the second variable.

Can you solve the following system of equations using the substitution method? x = y + 3 and x + y = 11.

Yes, by substituting x = y + 3 into the second equation (x + y = 11), we get y + 3 + y = 11, which simplifies to 2y = 8, so y = 4. Then, substituting y = 4 into x = y + 3 gives x = 7.

What is the elimination method for solving systems of linear equations?

The elimination method involves adding or subtracting two equations to eliminate one of the variables, making it easier to solve for the other variable.

Solve the following system of equations using the elimination method: x + y = 10 and x - y = 4.

By adding the two equations, we eliminate y: (x + y) + (x - y) = 10 + 4, which simplifies to 2x = 14, so x = 7. Then, substituting x = 7 into x + y = 10 gives y = 3.

What is the graphical method for solving a system of linear equations?

The graphical method involves plotting the equations on a coordinate plane and finding the point where the lines representing the equations intersect. This point of intersection is the solution to the system of equations.

Solve the system of equations using the graphical method: x + y = 8 and x - y = 2.

For the first equation, the intersection points are (8,0) and (0,8). For the second equation, the intersection points are (2,0) and (0,-2). After plotting these points and drawing the lines, the intersection point of the two lines is (5,3), which is the solution to the system.