## 12 Questions

What is the first step in solving a linear equation for a desired value?

Add or subtract to simplify the equation

In the elimination method for solving linear equations with two variables, what is the primary objective of adding or subtracting combinations of equations?

To simplify the equations and make calculations easier

In the substitution method for solving linear equations with two variables, what is the purpose of finding the value of one variable first?

To substitute it into the second equation

What is the final step in solving a linear equation once all fractions have been eliminated?

Solve for desired variable by isolating it on one side of the equation

Which method would be more appropriate for solving a system of linear equations where one variable can be easily isolated?

Substitution method

In solving linear equations with two variables, what is the purpose of writing an equation in terms of other variables?

To emphasize relationships between variables

What is a linear equation defined by?

An expression in one variable where the highest power of the variable is one

Which of the following is a linear equation?

$5x + 2 = 3$

What should you do first to solve a linear equation?

Simplify both sides of the equation

How do you eliminate fractions while solving a linear equation?

Multiply both sides by their LCM

Which step helps in isolating the unknown variable in a linear equation?

Simplify both sides of the equation

What characterizes a linear equation?

Having one variable with the highest power being one

## Study Notes

## Solving Linear Equations in Class 10 Maths

Linear equations play a crucial role in the field of mathematics, particularly during the course of study in high school algebra. They help us understand various mathematical concepts and their applications. In this article, we will discuss how to solve linear equations, which is a fundamental concept taught in class 10 maths.

### Understanding Linear Equations

A linear equation is defined by an expression in one variable where the highest power of the variable is one. For example, consider the following expressions: a) 2x + 3 = 5 b) y - 4 = x/3 c) z = 7 - t

The first two expressions are examples of linear equations with different variables (e.g., x or y), while the third one is a linear equation in terms of two variables (z and t).

### Steps for Solving Linear Equations

To solve a linear equation, follow these steps:

#### Step 1: Simplify both sides of the equation

You can simplify both sides using addition or subtraction rules. This step helps you isolate the value of the unknown variable (x, y, or z) on one side by getting rid of its exponents, if any, or by moving it to the left or right side depending on the sign used in this step.

#### Step 2: Get rid of fractions by multiplying both sides by their LCM

If there are any fractions present, you need to get rid of them using multiplication rules, applying the same operation for both sides and ensuring that the unknown variable remains unchanged.

#### Step 3: Solving the equation for the desired value

Once the equation has been simplified and all fractions have been eliminated, you can solve it easily. Depending on whether you want to find x, y, or z, you will either move that variable to one side of the equal sign or write the equation in terms of the other variables.

Here's an example problem to illustrate these steps:

```
Solve the following equation for x:
x + 5 = 9
Step 1: Subtract 5 from both sides of the equation to simplify it:
x + 5 - 5 = 9 - 5
x = 4
```

### Solving Linear Equations with Two Variables

Solving linear equations with two variables (e.g., z and t) involves using substitution or elimination methods. Let's discuss these methods one by one.

#### Substitution Method

The substitution method allows you to solve linear equations involving two variables by first solving for one of them, say z, and then plugging this value back into the equation that contains both variables, allowing you to find the other variable, say t.

For example, consider the following system of equations:

z + t = 10 z = x + 3

By solving the second equation for z, we get:

z = x + 3

Now, substitute z from the first equation into the second equation:

(x + 3) + t = 10 t = 10 - x - 3 t = 7 - x

This shows that the solutions for the linear equations with two variables can be found through substitution.

#### Elimination Method

The elimination method entails adding or subtracting certain combinations of the given equations to eliminate one of the variables, thus making it easier to solve for the remaining variable.

For instance, consider the system of equations:

z + t = 10 z = 3x - 5

In order to eliminate z, we add both equations:

((3x - 5) + (z)) + t = 10 3x - 5 + z + t = 10

Now, we can substitute z from the first equation into the second one:

3x - 5 + (3x + 3) + t = 10 t = 10 - 3x - 3 t = 7 - 3x

Thus, we have found the solutions for the linear equations with two variables using the elimination method.

In conclusion, solving linear equations in class 10 maths is an essential skill that helps students understand the concept of algebra and its applications. By following the steps outlined in this article and practicing with various problems, students can become proficient in solving linear equations and continue to develop their mathematical abilities.

Learn to solve linear equations in class 10 mathematics, a fundamental concept in algebra. Understand the steps involved in solving linear equations with one variable and with two variables through substitution and elimination methods. Practice problems to enhance your skills in solving linear equations.

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