Question

If the lines mx + ny = 4 and 6x+7y=5 represents a pair of coincident lines, then find the value of 2m-n​

Answer 1

Answer:

mx + ny = 4

6x + 7y = 5

are a pair of coincident lines.

For two lines to be coincident (a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0)

$\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }$

$\frac{m}{6} = \frac{n}{7} = \frac{4}{5}$

7m = 6n

5m = 24

m = 24/5

5n = 28

n = 28/5

2m = 48/5

So 2m - n = (48-28)/5 = 20/5 = 4.00

2m- n = 4.00

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Answer 2

Step-by-step explanation:

Given:-

The lines mx + ny = 4 and 6x+7y=5 represents a pair of coincident lines.

To find:-

Find the value of 2m-n ?

Solution:-

Given lines are mx + ny = 4

mx + ny -4 = 0------------(1)

On comparing with this a1x+b1y+c1 = 0 then

a1 = m ,b1= n and c1 = -4

and

6x+7y=5

6x + 7y - 5 = 0----------(2)

On comparing with this a2x+b2y+c2= 0 then

a2 = 6 ,b2 = 7 and c2 =-5

Given that the lines are coincident lines

=> The lines have infinitely number of many solutions

=>a1/a2 = b1/b2 = c1/c2

=> m/6 = n/7 = -4/-5

=> m/6 = n/7 = 4/5

Now

On taking m/6 = 4/5

=> 5×m = 4×6

=> 5m = 24

=> m = 24/5

The value of m =24/5

and on taking

n/7 = 4/5

=> 5×n = 4×7

=> 5n = 28

=>n = 28/5

The value of n = 28/5

Now the value of 2m - n

=> 2(24/5) - (28/5)

=> (48/5)-(28/5)

=> (48-28)/5

=> 20/5

=>4

2m-n = 4

Answer:-

The value of 2m-n for the given problem is 4

Used formulae:-

• If a1/a2 = b1/b2 = c1/c2 then the two lines a1x+b1y+c1=0 and a2x+b2y+c2=0 are consistent and dependent lines.

• They are coincident lines.

• They have infinitely number of many solutions.