Question

for what value of p x=2,y=3 is a solution of (p+1)x-(2p+3)y-1=0 and write the equation .how many solutions of this equation are possible? Is this line passes through point (-2,3)?give justification

Answer 1

explanation:

According to question

X=2,y=3

(p+1)2-(2p+3)3-1=0

2p+2-6p-9-1=0

2p-6p-9-1+2=0

-4p-10+2=0

-4p-8=0

-4p=8

p=8/-4=-2

p=-2

Next

Put the value of p=-2

(-2+1)2-(2×-2+3)3-1=0

(-1)2-(-1)3-1=0

-2+3-1=0

-3+3=0

0=0

Answer 2

The answers are

The value of p = -2

The required equation is x - y + 1 = 0

x - y + 1 = 0 will not pass through (-2,3)

Given:

x = 2, y = 3 is a solution of (p+1)x-(2p+3)y-1=0  

and (-2, 3) is a point

To find:

The equation

Check if the line passes through the point (-2,3)

Solution:

Given (p+1)x-(2p+3)y-1=0 ------(1)

The solution of given equation is x = 2 and y = 3

To find the value of p substitute x, y in given equation

at x = 2 and y = 3 equation(1)

⇒  (p+1)2-(2p+3)3-1 = 0  

⇒ 2p + 2 - 6p -9 - 1 = 0

⇒ -4p - 8 = 0

⇒  4p = -8

⇒  p = - 2

The value of p = -2

Now substitute p = -2 in (1)

⇒ (p+1)x-(2p+3)y-1 = 0

⇒ (-2+1)x - (2(-2) +3)y - 1 = 0

⇒  (-1)x - (-1)y - 1 = 0

⇒  -x +y - 1 = 0

⇒   x - y + 1 = 0

The required equation is x - y + 1 = 0

Now check if the line passes through the point (-2,3) by substitution in resultant equation

x - y + 1 = 0

⇒ - 2 -3 +1 = 0

⇒ - 4 $\neq$ 0

Here, we can conclude that x - y + 1 = 0 will not pass through (-2,3)

Therefore the answers are

The value of p = -2

The required equation is x - y + 1 = 0

x - y + 1 = 0 will not pass through (-2,3)

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