Question

If one equation of a pair of dependent linear equations is -3x+5y-2=0. The second equation will be:

6x+10y-4=0

6x-10y-4=0

6x+10y-4=0

-6x+10y+4=0​

Answer 1

Answer:

in the equation -3x+5y-2=0.let A1=-3,B1=5,C1=-2

We have A1/A2=B1/B2=C1/C2=1/k

wher k is the arbitrary constant.

by substituting the values we get

-3/A2=5/B2=-2/C2=1/k

we get A2=-3k,B2=5k,C2=-2k

put c=-2

we get A2=6,B2=-10,C2=4

so the second linear equation is 6x-10y+4=0

or we will get -6x+10y-4=0 if we put k=2

so there is no correct option

Answer 2

Given : one equation of a pair of dependent linear equations is -3x+5y-2=0

To Find :  The second equation will be:

Solution :  

Pair of linear equations

a₁x  +  b₁y + c₁  =  0

a₂x  +  b₂y + c₂  =  0

Consistent

if a₁/a₂ ≠ b₁/b₂   (unique solution  and lines intersects each others)

  a₁/a₂ = b₁/b₂ = c₁/c₂   (infinite solutions and line coincide each other )

Inconsistent

if  a₁/a₂ = b₁/b₂ ≠  c₁/c₂  ( No solution , lines are parallel to each other)

a pair of dependent linear equations Means a consistent system with Infinite solutions Hence

a₁/a₂ = b₁/b₂ = c₁/c₂ = k

So one of the Equation can be obtained by multiplying other equation with a non zero real number

-3x+5y-2=0

Multiply it by 2

-6x + 10y - 4 = 0  ( no such option given)

-3x+5y-2=0

Multiply it by -2

6x - 10y + 4 = 0  ( no such option given)

None of the given options is  correct

as option 1 and 3 are same  so possible that one of the option is

-6x + 10y  - 4 = 0  

Hence correct option would be -6x + 10y  - 4 = 0  

Learn More:

Show that system of equation 3x-5y=11 and 6x-10y=20 is inconsistent

brainly.in/question/8338977

for what value of a, the pair if linear equation. ax+3y=a-3,12x+ay=a ...

brainly.in/question/2517542