Pair of Linear Equations in Two Variables

**Recalling Linear Equations in One Variable**

We know that **algebraic expressions** are those that have a few numbers, letters and operators. For example, 2*x*, 3*y* + 4 and are all algebraic expressions and the letters *x*, *y* and *z* are the variables in the expressions.

If an algebraic expression is used for equating two different values or expressions, then it becomes an equation. For example, 2*x* = 4, 3*y* + 4 = 2*y* and are all equations.

Now, consider the equation 2*x* = 4. It has only one variable term, i.e., 2*x*. The [[mn:glossary]]exponent[[/mn:glossary]] of variable *x* is 1 and this is the highest exponent in the equation. We know that an equation having the highest exponent as 1 is known as a linear equation; so, 2*x* = 4 is a linear equation. Also, since the equation has only one variable *x*, it is a **linear equation in one variable**. Similarly, 3*y* + 4 = 2*y* and are also linear equations in one variable.

There are also equations having more than one variable. In this lesson, we will learn about linear equations in two variables.

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**Introduction to Linear Equations in Two Variables**

A linear equation comprising two different variables is called a **linear equation in two variables**. Let us consider the equation. This equation is used to compare the temperatures on the Celsius (*C*) and Fahrenheit (*F*) scales.

In the equation, *C* and *F* are both variables; thus, it is an equation in two variables. Also, the degree of the equation is 1, so it is a linear equation in two variables.

Other examples of linear equations in two variables: 3*x* − 4*y* = 4, and

The general form of a linear equation in two variables is **a****x**** + b****y**** + c = 0**. Here, *x* and *y* are variables while a, b and c are constants.

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The highest exponent of a variable involved in an equation is the degree of that equation.

For example, in the equation 3*y* + 4 = 2*y*, the highest exponent of variable *y* is 1; so, the degree of the equation is 1, or we can say that it is a **first-degree equation**.

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−40° is the only point at which the Celsius and Fahrenheit scales coincide.

So, −40°C = −40°F

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**Example: **

**Identify the linear equations in two variables among the following equations.**

i)

ii)

iii)

iv)

v)

**Solution**:

i) Since the equation consists of only one variable *x*, it is not a linear equation in two variables.

ii) The equation _{ }can be reduced to the general form of a linear equation in two variables, i.e., a*x* + b*y* + c = 0.

The equation is a first-degree equation and consists of two variables *t* and *D*. Thus, it is a linear equation in two variables.

iii) The equation consists of two variables *x* and *y*, but its degree is 2. Hence, it is not a linear equation in two variables.

iv) The equation can be reduced to the general fo...

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