__means finding the value of Y for the given value of X. If the equation is in the form of__

**Linear Equation****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

**,***and*

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

**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*.

__A system consisting of two simultaneous linear equations is said to inconsistent,__

**Inconsistent System:-***if it has no solution*

The two equations- * ax_{1} + by_{1} + c_{1} = 0* and

*are:*

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

(a)

*, if it has no solution*

**Parallel**(b)

*, if they have infinite number of solutions*

**Coincident**(c)

*, if they have one solution*

**Intersecting**

Important points for exams:

- 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** is called**m****x-coordinate**or**Abscissa**of Ais called**n****y-coordinate**or**Ordinate**of A.

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

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

*)*

**0,n****2k**

^{2}*For example: *Find the area of |x| + |y| = 6cm. The answer will be **2×6 ^{2} = 72 cm^{2}.**

#### How to draw Graph:

* – *Draw the graph of equation-

**4x-y = 2.**– Now, putting x=0 and y=0 at a time to find the intercepts.

– i.e.

**x-intercept = 2/4 = 1/2 ;**and

**y-intercept = -2**

And, if putting *x,y coordinates = 0*, LHS=RHS then the shaded region will on the *upper side *of the line, otherwise it will be on the *lower side *of the line.

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