Show that the system of equations ` - x + 2y + 2 = 0 and (1)/(2) x - (1)/(2) y - 1 = 0 ` has a unique solution.

It is true to say that the pair of equations - 2x + y + 3 =0 and 1/3 x + 2y -1=0 has a unique solution ? Justify your answer.

Show that the system 2 x + 3y - 1 = 0 , 4x + 6y - 4 = 0 has no solution.

Find all integers lambda for which the system of equations x+2y - 3z = 1,2x - lambday - 3z = 2x+2y + lambda z = 3 has a unique solution.

If the system of equations, a^(2) x - ay = 1 - a and bx + (3-2b) y = 3 + a possess a unique solution x = 1 , y = 1 , then

The value of a for which the system of equations , a^(3)x + (a + 1)^(3) y + (a + 2)^(3) z = 0 , ax + (a + 1) y + (a + 2) z = 0 & x+y+z=0 has a non - zero solution is :

The system x - 2y = 3 and 3x + ky = 1 has a unique solution, when

Show graphically that the following system of equations has no solutions x - 2y = 6 , 3x - 6y = 0

The system of equations x +2y+3z=1, x-y+4z=0, 2x+y+7z=1 has

The value of a for which system of equations , a^3x+(a+1)^3y+(a+2)^3z=0, ax+(a+1)y+(a+2)z=0, x + y + z = 0 , has a non-zero solution is:

The value of a for which system of equations , a^3x+(a+1)^3y+(a+2)^3z=0, ax+(a+1)y+(a+2)z=0, x + y + z = 0 , has a non-zero solution is: