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SUBSTITUTION

__SUBSTITUTION -__

**In algebra, substitution is a problem-solving technique where you replace one or more variables in an equation or expression with specific values or expressions in order to simplify the problem, solve for unknown values, or make the problem more manageable. Substitution is particularly useful when dealing with complex equations or expressions. Here's how the process of substitution typically works:**

__Identify the Variable to Be Substituted:-__Determine which variable in the equation or expression you want to replace with another value or expression. This variable is often the one you want to solve for or simplify.__Choose a Substitute:-__Decide what value or expression you want to substitute for the chosen variable. The substitute can be any expression or value that helps simplify the equation or expression. Common choices include constants, other variables, or algebraic expressions.__Perform the Substitution:-__Replace the chosen variable with the substitute throughout the equation or expression. Ensure that you apply the substitution consistently and correctly.__Simplify the Equation:-__After substitution, you may find that the equation becomes simpler and easier to solve or work with. Simplify the equation further if needed.__Solve for the Unknown:-__If your goal is to find the value of an unknown variable, proceed to solve the simplified equation for that variable. This may involve additional algebraic steps.__Check Your Solution:-__After solving, it's crucial to check your solution by substituting the value back into the original equation to ensure that it satisfies the equation's conditions.

**Here are some examples of how substitution can be used in algebra:-**

**Example.1) Solving an Equation Consider the equation: 3x + 2 = 11.**

**Ans.) To solve for "x," you can use substitution:**

**Substitute 2 for "x," as an initial guess.****Evaluate the left side of the equation: 3(2) + 2 = 6 + 2 = 8.****Compare the result to the right side of the equation: 8 ≠ 11.****Adjust the guess:- Substitute 3 for "x."****Evaluate again: 3(3) + 2 = 9 + 2 = 11.****The solution is confirmed: x = 3.**

**Example.2) Simplifying an Expression Consider the expression: 2x²+ 3x - 5. **

**Ans.) To simplify it, you can use substitution:**

**Let u = 2x². Now, the expression becomes u + 3x - 5.****Simplify the expression: u + 3x - 5.****Replace u with its original value: 2x²+ 3x - 5.**

**Example.3) Say you are given an Expression X-2**

**You have to find out the value of the Variable
X or Unknown quantity X by Substitution method, Given Value of X = 6.**

**Ans.) How will you go about it?**

**You have to put the given value of X which is 6 in this case, or substitute the value of X in the expression X - 2**

**= 6 -2**

**= 4 (Ans.)**

**Example.4) Similarly find the value
of X in the expression 10/X + 4 where the value of X is 2 **

**Ans.) By substituting 2 in place of the variable X we
get 10/2 + 4**

**= 5 + 4**

**= 9 (Ans.)**

**Example.5) Find the value of Variable or
unknown X in the Expression X + X/2. Given the value of X
= 5.**

**Ans.) By substituting the value of X
= 5
We get 5 + 5/2**

**= 5/1 + 5/2**

**= 5 + 2.5**

**= 7.5**

**or by finding
out the LCM which is 2 We get
10 + 5 = 15/2 which is also = 7.5 The earlier method is the shortest.**

**Both are correct. (Ans.) **

**Substitution is a valuable technique in algebra and is commonly used to simplify equations, solve systems of equations, and manipulate expressions to make them more manageable. It allows you to break down complex problems into simpler steps and can be a powerful tool in problem-solving.**