Linear Equations with One Variable

People use linear equations on a regular basis even if they don’t use a line graph since the conditions they encounter may involve an unknown number that may be expressed as a linear equation, such as calculating mileage rates, and income over time, and so on.

Definition of Linear Equation with one variable

Linear equations in one variable are equations in which there is only one variable and only one solution. It appears to be a straight line when plotted on a graph, either horizontally or vertically.

The simplest equation used to express and solve for an unknown quantity is a linear equation in one variable. It is usually a straight line and is readily illustrated visually. A linear equation with one variable is a simple technique to write a real-life problem in a mathematical proposition. Unknown quantities are represented by any variable or symbol, however, in most cases, the unknown quantity in a linear equation in one variable is represented by the variable ‘x.’ There are several easy approaches for solving a linear equation. To acquire the final value of the unknown quantity, the variables are isolated on one side of the equation and the constants are isolated on the other. A linear equation is one in which each variable in the equation has the same degree. 

Standard Form of Linear Equation with one variable.

A way of formulating linear equations is known as the standard form. The standard form, the slope-intercept form, and the point-slope form are all ways to write a linear equation. The general form of linear equations is Ax + By = C, which is also known as the standard form.

A linear equation is an equation in which the maximum power of the variable is one(1). 

For example, 4x + y = 6 is a linear equation, because the maximum power of both x and y is 1. The conventional form of a linear equation is Ax + By = C, where A, B, and C are all integers, and x and y are the variables.

Linear Equations with One Variable are Applied in Maths

Linear Equations with one variable are applied in maths in such a way that it helps to evaluate the value of an unknown quantity with the help of a known quantity.

• Convert the statement of the problem into a mathematical statement and arrange it as an algebraic expression that perfectly illustrates the problem.

• Analyse the unknowns in the problem and assign variables to these unknown quantities (quantities whose value might change based on the mathematical context).

• Examine the issue several times and make notes on the facts, phrases, and keywords. Sequentially organize the facts you’ve gathered.

• Write an equation using the algebraic expression and the facts in the problem statement, and solve it using systematic equation solving methods.

• Retrace your solution back to the problem and see if it satisfies the problem’s conditions.

These all are the basic uses of Linear equations with one variable that can be applied in mathematics, along with this, the linear equations can be used to calculate,

• Age-related problems: In this case, we make a linear equation in one variable with given known and unknown age: 

• Problems involving geometry: In this case, we make a linear equation in one variable with given known and unknown dimensions or relations between the quantities

• Problems of percentages: In this case, we make a linear equation in one variable with a given relation between a known quantity and an unknown quantity.

• Problems with work, time, and salary: In this case, we make a linear equation in one variable with a given known value to calculate the unknown one.

Point to Remember

• In linear equations with one variable, the degree of the variable should be exactly one.

• A straight line, either horizontal or vertical, is the graph of a linear equation in one variable.

• Any quantity added, subtracted, multiplied, or divided into both sides of a linear equation in one variable has no effect on the result.