# HOW TO ADD LINEAR EXPRESSIONS

How to add linear expressions :

Adding linear expressions means, combining the like terms in the given expressions.

To add any two or more linear expressions, we follow two methods

(i) Horizontal method

(ii) vertical method

In horizontal method, we should write the given expressions in a line and combine the like terms according to their signs.

In a vertical method, we should write the given algebraic expression vertically and combine.

Let us see some examples to understand how to add linear expressions.

Example 1 :

Add -6p - 8 and -3p - 6

Solution :

Horizontal method :

=  (-6p - 8) + (-3p - 6)

=  -6p - 8 - 3p - 6

=  -6p - 3p - 8 - 6

=  -9p - 14

Vertical method :

Hence -9p - 14 is the sum of the above linear expressions.

Example 2 :

Add -8r - 2 and 4r - 3

Solution :

Horizontal method :

=  (-8r - 2) + (4r - 3)

=  -8r - 2 + 4r - 3

=  -8r + 4r - 2 - 3

=  -4r -  1

Vertical method :

Hence -4r - 1 is the sum of the above linear expressions.

Example 3 :

Add -z - 8 and 6z - 5

Solution :

Horizontal method :

=  (-z - 8) + (6z - 5)

=  -z - 8 + 6z - 5

=  -z + 6z - 8 - 5

=  5z -  13

Vertical method :

Hence 5z - 13 is the sum of the above linear expressions.

Example 4 :

Add s + t,  2s - t, -s + t

Solution :

Horizontal method :

=  (s + t) + (2s - t) +  (-s + t)

=  s + 2s - s + t - t + t

=  2s + t

Vertical method :

Hence 2s + t is the sum of the above linear expressions.

Example 5 :

Add 3a - 2b and 2p + 3q

Solution :

=  (3a - 2b) + (2p + 3q)

=  3a - 2b + 2p + 3q

Hence 3a - 2b + 2p + 3q is the sum of the above linear expressions.

Example 6 :

Add 2a + 5b + 7, 8a - 3b + 3, - 5a - 7b - 6

Solution :

=  (2a + 5b + 7) + (8a - 3b + 3) + (- 5a - 7b - 6)

=  2a  + 8a - 5a + 5b - 3b  - 7b + 7 + 3 - 6

=  10a  - 5a + 5b - 10b + 10 - 6

=  5a - 5b + 4

Hence 5a - 5b + 4 is the sum of the above linear expressions.

Example 7 :

Add 6x + 7y + 3,- 8x - y - 7, 4x - 4y + 2

Solution :

=  (6x + 7y + 3)  + (- 8x - y - 7) + (4x - 4y + 2)

=  6x + 7y + 3 - 8x - y - 7 + 4x - 4y + 2

=  6x - 8x + 4x + 7y - y - 4y + 3 - 7 + 2

=  10x - 8x + 7y - 5y + 5 - 7

=  2x + 2y - 2

Hence 2x + 2y - 2 is the sum of the above linear expressions.

Example 8 :

Add (6a - 3b) and (7a - 5b)

Solution :

=  (6a - 3b) + (7a - 5b)

=  6a - 3b + 7a - 5b

=  3a + 2b

Hence 3a + 2b is the sum of the above linear expressions.

After having gone through the stuff given above, we hope that the students would have understood "How to add linear expressions".

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