Question

4x+py=-8
2x+2y=-2
having unique solution .find P​

Answer 1

Step-by-step explanation:

When there is unique solution then it must satisfy the property of coincident lines.

A1/A2not =b1/b2

4/2not=p/2

8not=2p

pnot=4

value of p can be any real no. except 4.

Answer 2

Step-by-step explanation:

Given :-

4x+py=-8

2x+2y=-2 having unique solution

To find :-

Find the value of p ?

Solution

Given pair of linear equations in two variables are

4x+py = -8

=> 4x+py+8 = 0

On comparing this with a1x+b1y+c1 = 0

a1 = 4

b1 = p

c1 = 8

and

2x+2y=-2

=> 2(x+y) = -2

=> x+y = -2/2

=> x+y = -1

=> x+y+1 = 0

On comparing this with a2x+b2y+c2 = 0

a2 = 1

b2 = 1

c2 = 1

we have

a1/a2 = 4/1 = 4

b1/b2 = p/1 = p

c1/c2 = 8/1 = 8

Given that

The equations having a unique solution.

We know that

a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are pair of linear equations in two variables if a1/a2 ≠ b1/b2 then they have a unique solution.

We have

a1/a2 ≠ b1/b2

=> 4 ≠p

=> p ≠ 4

Therefore , p does not equal to 4

Answer :-

The value of p is not equal to 4 i.e.if the value of p except 4 then the given equations having a unique solution

Used formulae:-

a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are pair of linear equations in two variables

• if a1/a2 ≠ b1/b2 then they have a unique solution.

Points to know :-

a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are pair of linear equations in two variables

• if a1/a2 ≠ b1/b2 then they are consistent and independent lines or Intersecting lines with a unique solution.

• if a1/a2 = b1/b2 = c1/c2 then they are consistent and dependent lines or Coincident lines with a unique solution.

• if a1/a2 = b1/b2 ≠ c1/c2 then they are inconsistent lines or Parallel lines or with no solution.