**Linear Equation** means finding the value of Y for the given value of X. If the equation is in the form of

**Y = MX + B**, with

**Y** &

**X** are the variables, and

**M** &

**B** are the rational numbers.

####
General Form:

In general form,

**y = mx +b** where y and x can not be zero and y>0. The graph of the equation is a straight line, and every straight line can be represented by an equation in the above form.

####
Slope-Intercept form:

**y = mx + b **or** ax + by + c = 0**
where,

**m** is the slope or gradient and

**b** is the Y-intercept constant.

**for example:** *y = 2x +1*, then

**m = 2 **&

** b = 1. or **
*3y = 2x - 3***, **then

** y = (2/3)x -3/2 => m = 2/3 **and

** b = -3/2**
####
Conditions for Solvability:

**y = mx + b **or** ax + by + c = 0**
the system of equation is

**ax**_{1} + by_{1} + c_{1} = 0 and

**ax**_{2} + by_{2} + c_{2} = 0
(i) a

__unique solution__, if

**a**_{1}/a_{2} ≠ b_{1}/b_{2}
(ii) an

__infinite number of solutions__, if

**a**_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2}
(iii)

__no solution__, if

**a**_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2}
**Consistent System:-** A system consisting of two simultaneous linear equations is said to be consistent

*, if it has one solution*.

**Inconsistent System:-** A system consisting of two simultaneous linear equations is said to inconsistent,

*if it has no solution*
The two equations-

**ax**_{1} + by_{1} + c_{1} = 0 and

**ax**_{2} + by_{2} + c_{2} = 0 are:

* *
(a)

**Parallel**, if it has no solution

(b)

**Coincident**, if they have infinite number of solutions

(c)

**Intersecting**, if they have one solution

* *
Important points for exams:

1. Coordinate points in a plane:
- Let,
**A** be a point in plane
- Let,
**m** and **n** are the distance of A from x-axis and y-axis respectively
- Then, the coordinate of A will be (
**m,n**).
**m **is called **x-coordinate **or **Abscissa **of A
**n **is called **y-coordinate **or **Ordinate **of A.

2. Coordinate point on x-axis: On X-axis, the y-coordinate or ordinate point will be

**Zero. **Hence, the straight line will pass through x-coordinate only,

*parallel to y-axis*. And, the coordinate of plane on x-axis will be (

**m,0**)

3. Coordinate point on y-axis: On Y-axis, the x-coordinate or abscissa point will be

**Zero. **Hence, the straight line will pass through y-coordinate only,

*parallel to x-axis*. And, the coordinate of plane on y-axis will be (

**0,n**)

4. The area bounded by |x| + |y| = k is **2k**^{2}.

Find the area of |x| + |y| = 6cm. The answer will be

- Now, putting x=0 and y=0 at a time to find the intercepts.

- i.e.

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