# Evaluate an Algebraic Expression

Any equation can be evaluated algebraically depending on the number of variables are there in that equation. If we consider a linear equation then there is only one variable connected to it so this can solved algebraically. If there are two variables x and y in the equation then it has to involve two equations so that we can solve this algebraic equation mainly using elimination and substitution method.

## Evaluating an algebraic expression

An algebraic expression may refer to constants or variables or the combinations of both with associated operators. Variables are used to represent unknown quantities. Therefore an expression is dumb, in the sense, you do not know what its magnitude could be. But you give life to an expression when you assign some values to the variable and this process is known as evaluating an algebraic expression. We will explain how do you evaluate an algebraic expression with a simple examples.

## Solved Examples

Question 1: Solve for x,  3x + 6 = 9.
(Example of a Linear Algebraic Equation)

Solution:
Given linear algebraic expression, 3x + 6 = 9

Step 1 :

Transport  6 to the right side so that the sign changes from positive to negative

=> 3x = 9 - 6

=> 3x = 3

Step 2:
Divide each side by 3, to isolate x,

=> $\frac{3x}{3} = \frac{3}{3}$

Question 2: Solve: X2 + 2 = 11
(Example of  a Pure Quadratic Equation)

Solution:
Given quadratic algebraic expression,  X2 + 2 = 11

Step 1 :

Solve for x,
=> X2 + 2 = 11

Subtract 2 from both sides

=> X2 + 2 - 2 = 11 - 2

=> x2 = 9

or x2 = 32

Step 2:
Taking square root both side

$(x^2)^\frac{1}{2} = (3^2)^\frac{1}{2}$

=> X = $\pm$ 3

or x = 3 and X = - 3.

Hence the values of x are: - 3 and 3.

(This contains two solutions as this is a pure quadratic equation).

Question 3: Solve:
x + y = 8 and x - y = 8
(Example of linear expression with two variables)

Solution:
Given system of linear equations
x + y = 8                                    .............................(1)

x - y = 8                                    ...............................(2)

Step1 :

Solve equation (1) and (2)

Choose equation (1), to transpose 'y' variable to right side with sign change

=> x = 8 - y                             ...............................(3)

Step 2:

Put equation (3) in equation in (2).

=> (8 - y) - y = 8

=> 8 - y - y = 8

=> 8 - 2y = 8

=> - 2y = 8 - 8 = 0

=> y = 0

Step3 :

Put the value of y in equation (1)

=> x + 0 = 8

=> x = 8

Hence the solution of the system is (x, y) = (8, 0).