Pair of Linear Equations in Two Variables

Study Notes

Pair of Linear Equations in Two Variables

A pair of linear equations in two variables is a set of two equations containing two variables, often represented by the letters x and y. These equations can be written in the form of ax + by = c, where a, b, and c are constants. In other words, the equations are of the form y = mx + b.

Solving a Pair of Linear Equations

To solve a pair of linear equations, you can use the following methods:

Graphical method: Plot the equations on a graph and find the point of intersection.
Substitution method: Solve one equation for one variable and substitute it into the other equation.
Elimination method: Add or subtract the equations to eliminate one variable.

Applications of Linear Equations

Linear equations have numerous practical applications in various fields, such as:

Physics: Linear equations are used to describe the motion of objects, including acceleration, velocity, and displacement.
Economics: Linear equations can model supply and demand curves, which help economists analyze market trends and predict future prices.
Engineering: Engineers often encounter linear equations when designing structures or analyzing circuits.

Examples of Linear Equations in Two Variables

Here are some examples of pairs of linear equations in two variables:

Example 1: Solve the system of equations x + y = 5 and 2x - 3y = 9.
Example 2: Solve the system of equations 3x + 2y = 6 and 2x - 3y = 9.
Example 3: Given the system of equations 2x + y = 14 and 3x - y = 6, find the possible values of x and y.

Description

Learn about pairs of linear equations in two variables, where two equations with two variables are solved using methods like graphical, substitution, and elimination. Explore the practical applications of linear equations in fields such as physics, economics, and engineering. Practice solving examples of linear equations involving x and y.