Question

2-13) Find the value of p for which the graphical representation of the following pair of linear equation
coincident lines.
X+ 2y + 5 = 0 and 2x + py + 10 = 0.​

Answer 1

GIVEN :

Equations :

x + 2y + 5 = 0 and 2x + py + 10 = 0.

The graphical representation of these equations is coincident lines.

For coincident lines, there are infinite solutions.

We know that when there are infinite solutions,

Then,

a1/a2 = b1/b2 = c1/c2

a1 = 1 a2 = 2

b1 = 2 b2 = p

=> 1/2 = 2/p

=> 1 × p = 2 × 2

=> p = 4

Therefore, the value of p is 4.

Answer 2

Answer :-

P = 4

Explanation :-

Equation 1 => x + 2y + 5 = 0

x1 = 1

y2 = 2

z3 = 5

____________________________

Equation 2 => 2x + py + 10 = 0

x2 = 2

y2 = p

z3 = 10

GIVEN :-

As it is given that lines are coincident , So now the line are on each other .

so, we have the formula

x1/x2 = y2/y2 = z1/z2

_________[Put values]_________

1/2 = 2/p

1/2 = 2/p

p = 4

So, we have the value of p as 4