Question

Pls. solve question no. 12


Lazy answers will be deleted!

Answer 1

3x–5y=2 for 3part
6x–10y=2 for 2part
4x–5y for 1part.

Answer 2

Hi there !

the standard form of a linear equation is 
ax + by + c = 0
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3x - 5y = 1
writing in standard form :-

3x - 5y - 1 = 0

a₁ = 3  , b₁ = -5  , c₁ = -1

for two lines of a graph to intersect ,
a₁/a₂ ≠  b₁ /b₂   

we have to form such linear equation !

3x - 5y - 1 = 0

a₁ = 3  , b₁ = -5  , c₁ = -1

6x - 4y  - 5 = 0
a₂ = 6  ,  b₂ = -4 , c₂ = -5

here ,
a₁/a₂ = 3/6
b₁ /b₂  = -5/-4 = 5/4

hence ,
a₁/a₂ ≠  b₁ /b₂   

hence the equations are :-
3x - 5y - 1 = 0
6x - 4y  - 5 = 0

when two lines are intersecting , they have only one solution [ unique solution]
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for two lines to be coincident lines , their coefficients must satisfy  :-
a₁/a₂ = b₁/b₂ = c₁/c₂

3x - 5y - 1 = 0
a₁ = 3  , b₁ = -5  , c₁ = -1

we have to form equations with coefficients so that their ratio is same .

6x - 10y  -2 = 0
a₂ = 6   , b₂ = -10  , c₂ = -2

a₁/a₂ = 3/6 = 1/2
b₁/b₂ =  -5/-10 = 5/10 = 1/2
c₁/c₂ = -1/-1=2 = 1/2

hence ,
a₁/a₂ = b₁/b₂ = c₁/c₂

so the equations that have its graphical representation as coincident lines are :-
3x - 5y - 1 = 0
6x - 10y  -2 = 0
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for a system of equations to have its graphical representation as parallel lines :-

a₁/a₂ = b₁/b₂ ≠  c₁/c₂


3x - 5y - 1 = 0
a₁ = 3  , b₁ = -5  , c₁ = -1

we have to chose the coefficients in a manner that the ratio of first two are equal but is not equal to third one !

6x - 10y  -7 = 0
a₂ = 6   , b₂ = -10  , c₂ = -7


a₁/a₂ = 3/6 = 1/2
b₁/b₂ =  -5/-10 = 5/10 = 1/2
c₁/c₂ = -1/-7 = 1/7

hence , 
a₁/a₂ = b₁/b₂ ≠  c₁/c₂

so the equations are :-

3x - 5y - 1 = 0
6x - 10y  -7 = 0

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