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.

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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,

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

=> x = 1. **answer**

Step 1 :

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

=> 3x = 9 - 6

=> 3x = 3

Divide each side by 3, to isolate x,

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

Given quadratic algebraic expression, X^{2} + 2 = 11

Step 1 :

Solve for x,

=> X^{2} + 2 = 11

Subtract 2 from both sides

=> X^{2} + 2 - 2 = 11 - 2

=> x^{2} = 9

or x^{2} = 3^{2}

**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).

Step 1 :

Solve for x,

=> X

Subtract 2 from both sides

=> X

=> x

or x

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

=> 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).

x + y = 8 and x - y = 8

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).**

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