Linear equations





Linear Equations is one of the branch of Algebra

ax+b, or ax+by+c or ax+by+cz+d are called linear expression, where x,y and z are called variables, a, b, c and d are constants.

An equation is a condition on variable.

And also it is an algebraic expression in which each term is a constant or with a product of a variable.

For example

2x+5 = 0 is an equation in one variable.

3x+4y+6 = 0 is in two variables.

Solving linear equations in one variable:

1) Solve for x: 3x-6=0

Here -6 is a constant added with 3x term.

To remove that constant let us add 6 on both sides.

3x-6+6 = 0+6 = 6

3x = 6

x = 6/3 =2

so x=2 is the solution.


2) Solve: 2x-5=15

Here we have -5 added to 2x term

2x-5 = 15

Adding 5 on both sides

2x-5+5 = 15+5

2x = 20

Dividing by 2

2x/2 = 20/2

X = 10


3) Solve : 5x - 2 = 2x – 6

To solve, let us subtract -2x on both sides

5x-2x - 2 = -6

3x - 2 = -6

Adding 2 on both the sides

3x - 2 + 2 = -6 + 2

3x = -4

3x = -4

Now we have to divide it by -4 on both sides.So that we are getting x =-4/3

So x = -4/3 is the solution.


4) Solve: 2x-5=15

Here we have -5 added to 2x term

2x-5 = 15

Adding 5 on both sides

2x-5+5 = 15+5

2x = 20

Dividing by 2

2x/2 = 20/2

X = 10


5) Solve: 5y + 3 = -8 + 3y

Here we have to subtract by -3y on both sides

5y -3y + 3 = -8

2y + 3 = -8

Now we have to subtract by -3 on both sides

2y + 3 -3 = -8 -3

2y = -11

Dividing by 2

2y/2 = 11/2

y = 11/2

There fore 11/2 is the solution for this variable y.