Linear Equations

The linear equation in one variable is an equation that is signified in the form of ax+b = 0. Here a and b are two given integers, and x is a variable that has only one clarification. For instance, 2x+3=8 is a linear equation consisting of a single variable in it. Hence, this equation has only one answer, which is x = 5/2. Whereas if we talk about a linear equation that has two variables, it will have two solutions.

What is Linear Equation in One Variable?

A linear equation in one variable is an equation that has only one variable of order number 1. It is of the standard form ax + b = 0, where x is the given variable.

This equation has only one accurate solution. A few examples are given below:

  • 6x = 1
  • 27x-1=0

Standard Form of Linear Equations in One Variable:

The standard and generic form of given linear equations in one variable are expressed as:

ax+b=0.

Where

  • ‘a’ and ‘b’ are the given real numbers.
  • Both ‘a’ and ‘b’ are not equivalent to zero.

Thus, the standard formula of any linear equation in one variable is ax + b = 0.

Solving Linear Equations in One Variable:

For solving an equation consisting of only one variable, the latter steps are followed:

  • Step 1: We use the LCM method and clear the fractions, if any.
  • Step 2: We simplify both sides of the given equation.
  • Step 3: We then isolate the variable given.
  • Step 4: Finally, we verify our answer.

FAQs

How many solutions does a linear equation in one variable have?

Every linear equation in one variable has only one and a unique solution. If the equation has two or more variables, then it will become a linear equation in two variables, linear equations in three variables, and so on. The number of solutions and clarifications modifies as per the count of variables in an equation that it contains.

What is the formula of a linear equation in one variable?

The formula or the approved form of an equation consisting of only one variable is given as ax + b = 0, as discussed earlier. Here, there is only one variable, that is x.

How to easily solve any equation having one variable?

First, we should put the variable on the left-hand side of the equation and the numerical values on the right-hand side of the given equation. Then we change the operators while switching the sides of the terms and finally solve the equation and get the answer for the variable.

In order to learn math and solve Linear equations in one variable one needs to focus on the fundamentals and solve a variety of worksheets online. Cuemath worksheets can help students understand the why behind every concept thus giving them an in-depth understanding of the topic.

Where can we use Linear Equations?

We can use Linear equations for the following operations and calculations:

  • For finding the midpoint of a given line segment
  • For finding the parallel and perpendicular lines
  • For finding the equation of a given line from two points on the graph

Equation of a line

There are various ways of expressing a given line. In the following subparts, a linear equation of the line is given in each specific case.

  • Slope–intercept form

Any non-vertical line can be expressed by its slope m and its y-intercept

  • Point–slope form

Any non-vertical line can be denoted by its slope m and the given coordinates 

  • Intercept form

Any line that is not parallel to the given axis and does not pass through the origin always cuts the axis in two not identical points. 

  • Two-point form
  • Determinant form

Conclusion 

Linear Equations are a very important topic in order to understand the concepts of geometrical calculations. Linear equations are, although very easy and simple to comprehend, but certain topics  might create confusion. Hence one would practice linear equations regularly in order to solidify their concepts and develop a rock-solid foundation.

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