Linear Equations Math

Introduction to linear equations in math:

A linear equations is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear equations can have one or more variables. Linear equations occur with great regularity in mathematics. The general form of the liner equation is y =mx +b. Otherwise it can be written as ax + by=c. Here we are going to how to solve the liner equation in math and its example problems. (Source from Wikipedia)


Solving method for linear equations in math:


Elimination method
Substitution method

Example problems for solving linear equations in math:


Example: 1

Solve the following liner equation using elimination method 2x+3y = 5 and x + y = 2

Solution:

2x+3y = 5 -----------------------1

x + y = 2 -------------------------2

Multiply equation(2) by 2, we get

2x + 2y = 4 ----------------------3

Take equation 1 and 3 subtract equation 3 from 1 we get

2x+3y = 5

2x + 2y = 4   (change the sign and add)

--------------------

y = 1

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Now we have to find the x value

Substitute y value in to the equation 1 we get

2x + 3y = 5

2x + 3 (1) = 5

2x + 3 = 5

Add both sides -3 we get

2x + 3 - 3 = 5 - 3

2x = 2

Divide both sides 2 we get

x = 1

Therefore the solution of the given liner equation is x = 1 and y = 1

Example: 2

Solve the following liner equation using substitution method

x+4y = 10

x+12y = 20

Solution:

x+4y = 10 ----------------------- 1

x+12y = 20 ----------------------2

Form equation 1 we can write

x = 10 - 4y -----------------------3

Substitute the x value into the equation 2

10-4y+12y = 20

10 + 8y = 20

Add both sides -10

8y = 20-10

8y = 10

y = `10 / 8`

y = `5/4`

Substitute y value into equation 3 we get

x = 10 – 4`(5/4)`

x = 10 -`20/4`

x = `(40 - 20) / 4`

x = `20/4`

x = 5

Therefore the solution of the given liner equation is x = 5 and y =` 5/4`