### Explanation

**Substitution of given values** is a fundamental concept in algebra and calculus where specific values are substituted into variables within mathematical expressions or equations. This technique is essential for solving equations, evaluating functions, and simplifying expressions.

When substituting, you replace each variable with its corresponding given value, then perform the necessary arithmetic operations to simplify the expression and find the result.

### Example 1: Simple Algebraic Expression

Given the expression $3x + 5$ and $x = 2$:

$3x + 5 = 3 \cdot 2 + 5 = 6 + 5 = 11$
### Example 2: Quadratic Equation

Consider the quadratic equation $ax^2 + bx + c = 0$ and substitute $a = 1$, $b = -3$, and $c = 2$:

$x^2 - 3x + 2 = 0$
### Example 3: Function Evaluation

For the function $f(x, y) = 2x^2 - y$, if $x = 3$ and $y = 1$:

$f(3, 1) = 2(3)^2 - 1 = 2 \cdot 9 - 1 = 18 - 1 = 17$
### Example 4: Multi-variable Equation

Given the equation $z = x^2 + y^2$ and substituting $x = 4$ and $y = 3$:

$\begin{aligned}
z &= x^2 + y^2 \\
&= 4^2 + 3^2 \\
&= 16 + 9 \\
&= 25
\end{aligned}$
### Importance

**Simplifies complex expressions**: By substituting specific values, we can reduce complex algebraic expressions to simple numerical results.
**Solves equations**: Helps in finding the numerical solutions of equations by substituting values of variables.
**Evaluates functions**: Allows the calculation of function outputs for given inputs.
**Applications**: Widely used in physics, engineering, economics, and various other fields for practical problem-solving.

### Steps to Substitute Given Values

**Identify the variables**: Determine which variables in the expression or equation need to be substituted.
**Substitute values**: Replace each variable with the given value.
**Simplify**: Perform arithmetic operations to simplify the result.
**Check**: Verify the calculations to ensure accuracy, especially in more complex expressions.