Linear equations in two variables are written in the ax + by + c = 0, where the coefficients a, b, and c would be for variables x and y, respectively.
This equation is ax + b + c = 0, where the coefficients are real numbers a, b, c. Solving an equation means finding the solutions. There can be infinitely many solutions to an equation with two variables.
Pair of linear equations:
The pair of two linear equations in two variables consists of two linear equations with similar variables.
Example:
- a1x + b1y + c1 = 0
- a2x + b2y + c2 = 0
Graphical method of solution of a pair of linear equations in two variables:
- Whenever two lines intersect at one specific point, the solution to the Linear Equation pair will be at that point alone. This is a consistent pair of equations.
- The two lines must coincide to have an infinite number of solutions. They are a consistent pair of equations.
- A line parallel to another line cannot solve a pair of linear equations with two variables. These are known as inconsistent pairs of equations.