The Power of Substitution in Mathematics: Simplify Expressions and Solve Equations

substitute

Substitution is a technique used in mathematics to replace a variable with an expression or value

Substitution is a technique used in mathematics to replace a variable with an expression or value. It can be used to simplify expressions or solve equations.

To substitute a variable in an expression, you replace the variable with the given expression or value and evaluate the resulting expression.

Here is an example to illustrate the process of substitution:

Suppose we have the expression 3x + 2y, and we are given that x = 2 and y = 5. To substitute these values into the expression, we replace x with 2 and y with 5:

3(2) + 2(5)

Now we can simplify this expression by performing the necessary arithmetic operations:

6 + 10

So the simplified expression after substitution is:

16

This means that when x = 2 and y = 5, the value of the expression 3x + 2y is 16.

Substitution can also be used to solve equations. For example, consider the equation 2x – 3 = 7. We can use substitution to find the value of x that satisfies this equation.

First, we substitute the right side of the equation with a variable. Let’s use the letter ‘a’ to represent the right side:

2x – 3 = a

Next, we substitute the given value for ‘a’ into the equation:

2x – 3 = 7

Now we solve for x by isolating the variable on one side of the equation:

2x = 7 + 3

2x = 10

x = 10/2

x = 5

So the solution to the equation 2x – 3 = 7 is x = 5, which we found using substitution.

In summary, substitution is a useful mathematical technique that allows us to replace variables with given expressions or values. It helps simplify expressions or solve equations by evaluating the resulting expressions or solving for the unknown variables.

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