An equation that represents a straight line in terms of two variables is called a linear equation in two variables.

The mathematical equations are formed in terms of two variables in some cases. If the two variables have exponent one, then the mathematical equation represents a straight line geometrically. Therefore, an equation, which expressed in two variables is called the linear equation in two variables.

$3x-4y+5 = 0$

It is an equation, which expressed in terms of $x$ and $y$. Now, write any variable in terms of remaining variable.

$\implies$ $3x+5 = 4y$

$\implies$ $4y = 3x+5$

$\implies$ $y = \dfrac{3x+5}{4}$

Get values of $y$ by substituting different values in $x$, and then draw a graph by the values of $x$ and $y$.

You observe that the graph displays a straight line. It is mainly due to exponent one of both variables. Hence, the equation is called as a linear equation.

Here is some more examples for the linear equations in two variables.

- $x-2y+6 = 0$
- $-4p+4q = -3$
- $7l-\sqrt{6}m-9 = 0$
- $-0.6y+5z = 2$
- $-8r-5s-4 = 0$

$a$, $b$ and $c$ are constants, and $x$ and $y$ are variables. The linear equations in two variables can be written mathematically in two ways in algebraic form.

- $ax+by+c = 0$
- $ax+by = c$

There are three methods in mathematics to solve the simultaneous linear equations in two variables.

- Substitution method
- Elimination method
- Cross multiplication method

Study each method with understandable solved problems to learn how to solve linear equations in two variables.

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