Class 10 Maths: Pair of Linear Equations in Two Variables Olympiad Questions

The linear equations are in the form of ax + by + c = 0. When we see the linear equations, then they are in the form of a straight line. In the above equation, a, b, & c are real numbers, in which a & b are not equal to zero. At the same time, x & y are the two variables. And c is the constant.

Pair of linear equations

When two linear equations are with each other, they are considered a pair of linear equations. In which both x & y terms are different from every equation.

• First equation: a1x + b1y + c = 0.
• Second equation: a2x + b2y + c = 0.

Graphical method

There are also some graphical methods to represent the linear equations in two variables. All these methods are discussed below:

• When two linear equations intersect at a single point, that point is the solution for the particular equations.
• When the two points coincide, there are infinite solutions to the linear equation on that point.
• And when both lines move parallel to each other, there is no solution for such an equation. Further, this pair is known as the inconsistent point.

Methods of solving equations

• Substitution method.
• Cross multiplication method.
• Elimination method.