In our notes for Class 8, we had learned about linear equations and simultaneous linear equations. We suggest that you quickly revise the basic concepts of linear equations and how to solve two such equations simultaneously.

Linear Equation in Two Variables

An equation of the form $ax + by + c = 0$, where $a, \ b, \ and \ c$ are real numbers $(a \ne 0, \ b \ne 0)$ is called a linear equation in two variables $x \ and \ y$. Such an equation has degree 1.

Two linear equations in two variables$\ x \ and \ y$  are said to form a system of simultaneous linear equations if each of them is satisfied by the same pair of values of  $\ x \ and \ y$.

You learned about the Substitution Method and Elimination Method for solving two linear equations simultaneously in Class 8. You could read that by clicking here.

There is another method called “Cross Multiplication Method” by which we could solve the linear equations too. In short, let

$ax_1+by_1 + c_1 = 0$

$ax_2+by_2 + c_2 = 0$

be a system of simultaneous linear equations in two variables $x$ and $y$ such that $\frac{a_1}{a_2}$ $\neq$ $\frac{b_1}{b_2}$ i.e. $a_1b_2 - a_2b_1 \neq 0$. Then the system has a unique solution given by

$\displaystyle x = \frac{b_1c_2-b_2c_1}{a_1b_2-a_2b_1} \text{ and } y = \frac{c_1a_2-c_2a_1}{a_1b_2-a_2b_1}$

You could choose any of the above three methods to solve simultaneous equations. You will get a hang of each one of these methods once you solve multiple questions. We have listed 50+ questions and their solutions for you to practice and get comfortable with the topic.