Question

is the pair of eqution X+2y-3=0;6y+3x-9=0consistent justify your answer​

Answer 1

Answer:

this is the answer hope it helps to you thank you

Answer 2

Explanation:

Given:-

X+2y-3=0

6y+3x-9=0

To find:-

Check whether the given pair of linear equations are consistent or not? Justify?

Solution:-

Given pair of linear equations in two variables:

X+2y-3 = 0

On Comparing this with a1x+b1y+c1 = 0

a1 = 1 ; b1 = 2 ; c1 = -3

and

6y+3x-9 = 0

=> 3x+6y-9 = 0

=> 3(x+2y-3) = 0

=> x+2y-3 = 0/3

=> x+2y-3 = 0

On Comparing this with a2x+b2y+c2=0

a2=1 ; b2=2 ; c2= -3

now

a1/a2 = 1/1 = 1

b1/b2 = 2/2 = 1

c1/c2 = -3/-3 = 3/3 = 1

a1/a2 = b1/b2 = c1/c2

They are consistent lines

Alternative Method:-

Given lines are X+2y-3 = 0 and 6y+3x-9 = 0

Since the second equation is obtained by multiplying with 2 so they are consistent and dependent lines.

Answer:-

The given lines are Consistent and dependent lines .

Used formulae:-

• a1x+b1y+c1=0 and a2x+b2y+c2=0 are the pair of linear equations in two variables, if a1/a2 = b1/b2 = c1/c2 then they are consistent and dependent lines.
• They are coincident lines.
• They have infinitely number of many solutions.
• If a1x+b1y+c1=0 and k(a1x+b1y+c1)=0 then they are consistent and dependent lines.