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.