The pair of equations `x + 2y + 5 = 0` and ` -3x - 6y + 1 = 0` has

Find the number of solutions for the pair of equations x + 3y + 5 =0 and - 3x - 9y + 2 =0.

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.

Show that the homogenous system of equations x - 2y + z = 0, x + y - z = 0, 3 x + 6y - 5z = 0 has a non-trivial solution. Also find the solution

Find the value of 'k' for which the pair of equations 2x - ky + 3 = 0. 4x + 6y - 5 = 0 represent parallel lines.

The pair of equations 2x-5y+4=0 and 2x+y-8=0 has

The value of k, so that the following system of equations 3x – y + 5 = 0 and 6x - 2y + k=0 has no solution, is

The pair of equations 2x+3y=5" and "4x+6y=15 has

The system of equations 3x + y -4=0 and 6x + 2y-8=0 has

Find the value(s) of p for the following pair of equations: 2x+ 3y-5=0 and px- 6y-8=0 , if the pair of equations has a unique solution.