# Basic Linear Equation concepts for CAT

# Linear Equation Concept to Crack Cat 2018

Linear Equation is one of the basic and fundamental topic in Quantitative section for cracking CAT. This is the most easiest of all and you can get full score in these questions in one attempt. The only way to do this is to practice and go through the concept and tricks shared below:

### Linear Equation Concept:

An equation whose solution is a straight line. In a linear equation, the variables are raised to the first power there are no variables in denominators, no variables to any power (other than one), and no variables under root signs.

**For Example**

2 x + 4 = 0 — equation (1)

Solving linear equations means finding out the unknown (usually only one but possibly several). In the above equation x is the unknown but there can be more than 2 or more variables (unknown) in a linear equations as given below.

2 x + 3 y = 12 — equation (2)

6 x +8 y +9 z =12 — equation (3)

So, A linear equation is an equation that can be written in the form y= a x + b where x and y are variables & a and b are constants. Note that the exponent on the variable of a linear equation is always 1.

These are examples of linear expressions:

x + 4

2 x + 4

2 x + 4 y

**To solve linear equations we will make heavy use of the following facts.**

- If
*a=b*then*a+c = b+c*for any c. All this is saying is that we can add a number, c, to both sides of the equation and not change the equation. - If
*a=b*then*a-c = b-c*for any c. As with the last property we can subtract a number, c, from both sides of an equation. - If
*a=b*then*ac = bc*for any c. Like addition and subtraction we can multiply both sides of an equation by a number, c, without changing the equation. - If
*a=b*then*a/c = b/c*for any non-zero c. We can divide both sides of an equation by a non-zero number, c, without changing the equation.

These facts form the basis of almost all the solving techniques that we’ll be looking so it’s very important that you know them and don’t forget about them. One way to think of these rules is the following. What we do to one side of an equation we have to do to the other side of the equation. If you remember that then you will

always get these facts correct.

#### Examples:

#### Solve for x :

6(2x – 5) = 4(8x + 7)

6(2x – 5) = 4(8x + 7)

12 x – 30 = 32 x+28

—–> To isolate the x ‘s on either side of the equation, you can either add –12 x to both sides

or add –32 x to both sides.

+12 x – 30 = 32 x + 28

—–> Subtract 12 x both the sides

– 30 = 20 x + 28

—–> Subtract 28 both the sides (isolate the 20 x)

-58 = 20 x

x= -58/20

x= -29/10

To Know more Concept and examples related to Linear Equation, Download the PDF Linear-eqn

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