Question

If the pair of lines 2x + 3y + 7 = 0 and ax + by + 14 = 0 are coincident
lines then the values of 'a' and 'b'are respectively equal to​

Answer 1

Step-by-step explanation:

a+b/2 = a+b-3/3 = 4a +b/7

a+b/2 = 4a + b/7

7(a+b) = 2(4a+b)

7a + 7b = 8a + 2b

a-5b =0

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Answer 2

Concept

Two lines are said to be coincident if one of them lies on the top of the other and vice versa. A system of linear equations represents the equation of lines. Suppose ax+by+c=0 and px+qy+r=0 are two linear equations which represent the lines then the necessary and sufficient condition for the two lines to coincide is given as,

a/p = b/q = c/r, where a,b,c,p,q and r are the coefficients respectively.

Given

2x+3y+7=0

ax+by+14=0

Find

We have to calculate the value of a and b respectively.

Solution

Using the above condition we have,

2/a = 3/b = 7/14

Taking first and last term, we have

2/a = 7/14

2/a = 1/2

a = 4

Now, taking second and last term we get

3/b = 7/14

3/b = 1/2

b = 6

Hence the calculated value of a and b is 4 and 6 respectively.

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