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NCERT Solutions for Class 10 Maths Chapter 3 CONDITIONS FOR SOLVABILITY

This content is part of NCERT Solutions for Class 10 Maths Chapter 3 Pairs of Linear Equations in Two Variables

CONDITIONS FOR SOLVABILITY (OR CONSISTENCY) OF SYSTEM OF EQUATIONS:

2.2          (a) Unique Solution :

Two lines a1 + b1y + c1 = 0 and a2x + b2y + c2 = 0, if the denominator a1b2 - a2b1 0 then the given system of equations have unique solution (i.e. only one solution) and solutions are said to be consistent.

               \     a1b2 - a2b1 0         Þ            

2.2 (b)  No Solution :

Two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, if the denominator a1b2 - a2b1 = 0 then the given system of equations have no solution and solutions are said to be consistent.

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NCERT Solutions for Class 10 Maths Chapter 1 EUCLID’S DIVISION ALGORITHM

This content is part of NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

EUCLID’S DIVISION ALGORITHM :

If ‘a’ and ‘b’ are positive integers such that a = bq + r, then every common divisor of ‘a’ and ‘b’ is a common divisor of ‘b’ and ‘r’ and vice-versa.

 Ex.4        Use Euclid’s division algorithm to find the H.C.F. of 196 and 38318.

Sol.         Applying Euclid’s division lemma to 196 and 38318.

               38318     = 195 × 196 + 98

               196          = 98 × 2 + 0

               The remainder at the second stage is zero. So, the H.C.F. of 38318 and 196 is 98.

 Ex.5        If the H.C.F. of 657 and 963 is expressible in the form 657x + 963 × (-15), find x.

Sol.         Applying Euclid’s division lemma on 657 and 963.

               963 = 657 × 1 + 306

               657 = 306 × 2 + 45

               306 = 45 × 6 + 36

               45 = 36 × 1 + 9

               36 = 9 × 4 + 0

               So, the H.C.F. of 657 and 963 is 9.

               Given : 657x + 963 × (-15) = H.C.F. of 657 and 963.

               657 x + 963 × (-15) = 9

               657 x      = 9 + 963 × 15

               657 x      = 14454                

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Purple Buddha Project recycles and transforms remains weapons of conflict in Cambodia, one of the most bombed countries in the history of mankind into jewelry through local fair-trade cooperatives, essentially transforming an object traditionally symbolizing negativity into positivity. 

Support the Purple Buddha Project today

Purple Buddha Project Homepage

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stream art!

tonight marks the second song tariff, and it was on the Gamzee cover of Toxic. karkalicious took 5 times to be tariffed, but this one took one and a half. that’s why the gamzee is there.

anywho, benis was REALLY impatient with, like, everyone tonight.

like. really impatient. she killed a lot of dudes just for saying some mean off-hand comments.

also, a couple of pics of benis on vacation, which are super cute!

the artists, in order:

https://onepeachymo.tumblr.com/

http://scezumin.tumblr.com/

https://dragonmons.tumblr.com/

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Tomato and Halloumi Bake with Courgette

Follow for recipes

Is this how you roll?

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