Simple Linear Relationship

Introduction to simple linear relationship:

Simple relationship between the linear function is explained with the help of linear algebra expressions and problems. A linear expression shows the relationship between the simple linear function. This relationship associates with the families of vectors called linear spaces, and the function has the relationship in the form of input one vector and output one vector, based to certain rules. Linear relationship has the demonstration in analytic geometry and their relations are generalized in operator theory. The problems with simple linear relationship are discussed below.

Example Problems in Simple Linear Relationship:

Example 1:

Reduce the linear equation -2(y - 3) – 4y - 1 = 3(y + 4) - y

Solution:

Given expression is
-2(y - 3) – 4y - 1 = 3(y + 4) - y

Multiplying the integer terms
-2y + 6 – 4y - 1 = 3y + 12 - y

Grouping the above terms
-6y + 5 = 2y + 12

Subtract 5 on both sides
-6y + 5 - 5 = 2y + 12 -5

Grouping the above terms
-6y = 2y + 7

Subtract 2x on both sides
-7y – 2y = 2y + 7 -2y

Grouping the above terms
-9y = 7

Multiply -1/9 on both sides
y = - 7/9

y = - 7/9 is the solution for the given equation

Example 2:

Reduce the linear function     -5(z + 2) = z + 9

Solution:

Given expression is
-5(z + 2) = z + 9

Multiplying the factors in left term
-5z - 10 = z + 9

Add 10 on both sides
-5z - 10 + 10 = z + 9 + 10

Grouping the above terms
-5z = z + 19

Subtract x on both sides
-5z - z = z + 19 -z

Grouping the above terms
-6z = 19

Multiply -1/6 on both sides
z = -19/6

z = -19/6 is the solution for the given equation

Practice Problems for Linear Relationship:

1) Reduce the linear equation -5(y - 3) – 2y - 3 = 2(y + 1) – 3y

Answer: y = 13/4 is the solution for the above given equation

2) Reduce the linear equation     -7(a - 2) – 2a - 2 = 5(a + 2) – 5a

Answer: a = 0 is the solution for the given equation