Linear eq

Interchanged coefficients
23x + 77y = 145
77x + 23y = 155

If x+y chahiye toh simply add both eqs & x-y chahiye toh subtract both eqs

Const difference:
3x + 5y + 7z = 30
2x + 5y + 8z = 25

No need of 3 eqs, Simply multiply eq 1 by diff of eq 2 and multiply eq 2 by diff of eq 1

System of linear eqs:

1. Unique sol

2. Infinite sol

3. No sol

Linear eq in 2 variable represents a ___

Unique sol: a1/a2 ≠ b1/b2

Infinite sol: a1/a2 = b1/b2 = c1/c2
No Sol: a1/a2 = b1/b2 ≠ c1/c2

Represents Line

Possible nos. of solutions

Start with largest coefficient and try to make it zero

Optimisation

Jisko find krna hai usko akela kro and jispe woh depend hai usko chhedo

If abc are distinct integers a + b + c = 18

Max value and min value

Max value will lie 5,6,7

Without distinct- 6,6,6

Calculate nos of solutions

(EP - SP)/ diff or gap + 1