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Linear Equations
Linear Equations in Two Variables A linear equation in two variables is an equation of the form: Ax + By = C where: A is a constant, which rep...
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Linear Equations in Two Variables A linear equation in two variables is an equation of the form: Ax + By = C where: A is a constant, which rep...
Linear Equations in Two Variables
A linear equation in two variables is an equation of the form:
Ax + By = C
where:
A is a constant, which represents the coefficient of the variable x
B is a constant, which represents the coefficient of the variable y
C is a constant
A linear equation represents a straight line in the coordinate plane. The line has a constant slope (A) and a constant y-intercept (C).
Solving Linear Equations:
To solve a linear equation for a variable, we need to isolate that variable on one side of the equation. This can be done by performing the following steps:
Subtract Ax from both sides of the equation.
Subtract By from both sides of the equation.
Divide both sides of the equation by A.
The resulting equation will give us the value of the variable in terms of the other variable.
Examples:
Example 1:
2x + 5 = 13
After solving the equation, we get:
x = 4
Example 2:
3y - 7 = 19
After solving the equation, we get:
y = 5
Applications of Linear Equations:
Linear equations are used in various real-world applications, including:
Predicting the future price of a stock or commodity
Determining the amount of money needed to pay a bill
Optimizing the route of a delivery truck
Modeling the spread of a disease
By understanding linear equations, we can make accurate predictions and solve real-world problems