Pair of linear equation s class 10 imp

 Question 1.

Draw the graph of 2x + y = 6 and 2x – y + 2 = 0. Shade the region bounded by these lines and x-axis. Find the area of the shaded region. [CBSE 2007]

Solution:

The given system of equation is
2x + y – 6 = 0 ………. (i)
2x – y + 2 = 0 ……… (ii)

 solutions for each equation of the system are:
(i) ⇒ y = 6 – 2x

Table of solutions for 2x + y – 6 = 0

Similarly 

Table of solutions for 2x – y + 2 = 0

Plotting these on the graph

These intersect at (1, 4), so this is the solution. 
In graph, area bounded by the lines and x-axis is

 ∆PAB which is shaded.

Draw PM ⊥ x-axis

PM = y-coordinate of P  (1, 4)    = 4 units

and AB = 1 + 3 = 4 units

∴ Area of shaded region

= Area of ∆PAB = 12 × AB × PM

= 12 × 4 × 4 = 8 sq. units.

Zero Tax Till 12 Lakhs

 Question comes in mind that when there is no tax till 12 

lakhs income in the latest union budget which will applicable from 1 April 25 then why 

these new tax slabs are introduced. 

Actually there is very simple 

calculation behind this. 

Government says that till the 

Income 12 lakhs these slaps will 

not be appreciate because one 

will be given rebate under 87 A. 

so ones tax will be zero. 

If one earns even Rs 1 extra 

then 12 lakhs then these slabs

will be appreciate. 

In this budget government is

giving standard deduction of 

Rs 75000 also, so we can say

that there will be zero Tax till

the income of 12,75,000.

standard deviation means 

first Rs 75000 will be deducted

from your income then you 

will get Taxable income. 

This is my understanding and

if you think that this is helpful

then Thanks , If you think that 

this is not true then you can 

make ne clear also by means

of comments.