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## Mathematics / Pair of Linear Equations in Two Variables

### Mathematics / Pair of Linear Equations in Two Variables

A linear equation is an algebraic equation that contains terms which can either be constants or variables. The variables can only be of the first power.

A linear equation in two variables is of the form ax + by + c = 0, where x and y are variables and a, b and c are real numbers. Additionally a and b are non zero.

The graph of a linear equation in two variables plotted on a Cartesian plane is a straight line.

Given a pair of linear equations, they can be plotted as two lines in the Cartesian plane.

• If the two lines intersect, the pair of equations is said to be consistent. Solving the two equations simultaneously yields a unique value for each of the two variables. These values represent the co-ordinates of the point of intersection.
• If the two lines are parallel, the equations are inconsistent and there is no solution.
• If the two lines are coincident, then there are infinite solutions since every point on these lines is a point of intersection and as we know the line extends infinitely.

Lessons
Topics
Lessons
Topics
• Introduction to Pair of Linear equations in two variables
• Pair of Linear Equations in Two Variables
• Graphical Representation of a Pair of Linear Equations
• Review of Pair of Linear equations in two variables
• Determinant method of solving simultaneous equations
• Condition of Consistency of Equations
• Graphical Method of Solving Simultaneous Linear Equations
• Algebraic Methods of Solving Simultaneous Linear Equations in Two Variables
• Applications to Word Problems
• ### Simultaneous Linear Equation in Two Variables

Learnhive Lesson on Simultaneous Linear Equation in Two Variables

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