Lesson

Title: Linear Equations with Two Variables

Grade: 1400-a Lesson: S1-L2

Explanation: Hello students, let us learn a new topic in SAT-2 today with definitions, concepts, examples, and worksheets included.

Lesson:

Definition: Linear Equation

A linear equation is an algebraic equation that represents a straight line on a coordinate plane.

It is an equation in which the highest power of the variable(s) is one.

The general form of a linear equation is:
ax + by = c

1

.

Explanation: Here, the given image shows that x and y are variables. The constants a and b represent the coefficients of the variables x and y, respectively, while c is the constant term.

Definition: Linear Equations with Two Variables

Linear equations with two variables are mathematical equations that involve two variables (usually represented by x and y) and are of the form :

The general form of a linear equation in two variables is:
ax + by = c

2

.

Explanation: There, the given image shows that constants a and b represent the coefficients of the variables x and y. The x and y are variables. While c is the constant term.

Definition: Methods of linear equation with two variables

1.Substitution method
2.Elimination method
3.cross multiplication method

3

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Explanation: Substitution method: Solve one equation for one variable and substitute it into the other equation. This reduces the system to a single variable equation, which can be solved quickly.

Elimination method: Multiply one or both equations by suitable constants to create opposite coefficients for one of the variables. Then, add or subtract the equations to eliminate one variable and solve for the other.

Cross-multiplication method: The cross-multiplication method is a technique used to solve linear equations with two variables, specifically equations in the form of fractions or proportions. It is a convenient method for solving equations involving ratios or proportions. Let’s consider an example equation: \$ (a/b) = (c/d) \$


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