**Linear inequalities in ordered pair**(1)The set of** ordered pair (x, y)** such that **ax+by < c (2)** And the set of **ordered pair (x, y)** such that **ax+by > c** the region one and two are** called half plane** and the line **ax+by=c** is called the** boundary of each half plane. **

**Vertical line in Linear inequalities ;**

** a vertical line** divides the plane into **left and right half plane.**

**NON-Vertical**** line in Linear inequalities ;**

**non-vertical line** divides the plane into **upper and lower half planes.**

A solution of linear inequalities in** x and y ordered pair** of number, which satisfies the inequalities.

**Linear inequalities in ordered pair:**

**EXAMPLE:**

**The ordered pair (1, 1**) is a solution of the inequality** x + 2y < 6** because **1+ 2(1)=3 < 6 which is true.**

**There are inequalities many ordered pairs** that satisfy the inequality **x + 2y < 6**, so its graph will be **half plane.**

**Corresponding Equation in inequalities: **

Linear inequalities **ax +by =c is called associated** Or **corresponding** equation of each of the above-mentioned inequalities.

EXAMPLE:

**Graph of inequality x + 2y < 6 **

**SOLUTION:**

The associated equation of inequality.

**(i) x +2y < 6**

**is **

** x + 2y = 6**

the line **(ii)** **intersect the x-axis and y-axis** at** (6, 0) and (o, 3)** respectively. As no point of the line **(ii)** is a solution of the inequality **(i)** , so the graph of the line **(ii)** is shown by using dashes. We take **o(0, 0)** is a test point because it is not on the line** (ii)**

substituting **x =0, y = 0** in the expression **x = 2y gives 0 – 2(0) =0<6** so the point (0,0) **satisfies the equation (i) **