If the equations p x+2 y-3=0, x+3 y-4=0 ...

If the equations `p x+2 y-3=0, x+3 y-4=0` and `p x^2+3 y^2+3 x y+(q-3) x-3 y-1=0(p ne 23)` has a unique solution then find the value of `(p+q)`.

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

DETERMINANTS
CENGAGE|Exercise Question Bank|23 Videos
DETERMINANT
CENGAGE|Exercise Multiple Correct Answer|5 Videos
DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS
CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

For what value of p the pair of linear equations (p + 2)x – (2p + 1)y = 3(2p – 1) and 2x – 3y = 7 has a unique solution.

Consider a Delta ABC whose sides AB,BC and CA are represented by the straight lines 2x+y=0,x+py=q and x-y=3 respectively.The point P is (2,3). If P is orthocentre,then find the value of (p+q) is

The values of p, for which the equations 6x + py - 5 = 0 and 3x + 2y - 8 = 0 have unique solution is :

If the area bounded by y = ||x|^(2) - 4|x| + 3|| and the x-axis from x = 1 to x = 3 is p/q (where, p & q are coprime) then the value of p + q is

If x + y = p and xy = q, then find the value of (1)/(x^(3)) + (1)/(y^(3)) will be

Find the values of p in (i) to (iv) and p and q in (v) for the following pair of equations (i) 3x - y - 5 = 0 and 6x - 2y - p = 0 , if the lines represented by these equations are parallel. (ii) -x + py = 1 and px - y = 1 , if the pair of equations has no solution. (iii) -3x + 5y = 7 and 2px - 3y = 1 , if the lines represented by these equations are intersecting at a unique point. (iv) 2x + 3y - 5 = 0 and px - 6y - 8 = 0 , if the pair of equations has a unique solution. (v) 2x + 3y = 7 and 2px + py = 28 - qy , if the pair of equations has infinitely many solutions.

If the lines p_1 x + q_1 y = 1, p_2 x + q_2 y=1 and p_3 x + q_3 y = 1 be concurrent, show that the points (p_1 , q_1), (p_2 , q_2 ) and (p_3 , q_3) are colliner.

CENGAGE-DETERMINANTS-Question Bank

If |[sqrt(3) x-x^2, x-1 , x-sqrt3], [sqrt3 x , x , sqrt3-1] ,[x-1, ...
Text Solution
|
If f(x)=|cos (x+alpha) , cos (x+beta) , cos (x+gamma)],[ sin (x+alpha...
Text Solution
|
If the equations p x+2 y-3=0, x+3 y-4=0 and p x^2+3 y^2+3 x y+(q-3) x-...
Text Solution
|
Let f(x)=|[1+sin ^2 x, cos ^2 x , 4 sin 2 x],[ sin ^2 x ,1+cos ^2 x...
Text Solution
|
Given 2 x-y+2 z=1 , x-2 y+z=-4 , and x+y+lambda z =4. Then the. value ...
Text Solution
|
If M and m are maximum and minimum value, respectively of |[1 , cos th...
Text Solution
|
The value of |[log (3) 512 , log (4) 3 ],[ log (3) 8 , log (4) 9]||[...
Text Solution
|
If x in[0, (pi)/2] such that |(sin x+cos x)-sqrt2| +|y+(1)/(y)-2|+|z| ...
Text Solution
|
If alpha, beta, gamma are roots of the equation x^3+x^2+2 x-4=0, then ...
Text Solution
|
If p and q are real so that sysiem of equations p x+4 y +z=0,2 y+3 z=1...
Text Solution
|
If |[1 , x, x^2],[ x , x^2 , 1],[ x^2 , 1 , x]|=3, then the value ...
Text Solution
|
Let f(x) = |[x,1,(-3)/(2)],[2,2,1],[(1)/(x-1) ,0,(1)/(2)]| . The miniu...
Text Solution
|
In the determinant, Delta=|[-2, 5 , -1],[ 4 , 7, 0],[ 5, -3, 1]|...
Text Solution
|
If |[x^2, x^4 , (x-1)^2],[ 0, 4, 6 x^2 ],[ 4 ,1,7] |= overset(6) ...
Text Solution
|
If a, b, c are the sides of a scalene triangle such that |[a , a^2 , a...
Text Solution
|
Number of real roots of the equation |[sin x , x], [1 , 1]||[cos x, ...
Text Solution
|
Let a+b+c=s and |[s+c, a, b],[ c ,s+a, b],[ c, a , s+b]|is cqua...
Text Solution
|
In triangle A B C, if |[1, a, b],[ 1 , c, a],[ 1, b, c]|=0 then...
Text Solution
|
If system of linear equations (a-1) x+z=alpha1 x+(b-1) y=beta and y+(c...
Text Solution
|
If a1, a2, a3, 5,4, a6, a7, a8, a9 are in H . P, then the value of the...
Text Solution
|