Maths (commerce) Solve the Following Question.(3 Marks)

Find the value(s) of k, if the following equations are consistent.

(ii) kx + 3y + 4 = 0, x + ky + 3 = 0, 3x + 4y + 5 = 0

Find the value(s) of k, if the following equations are consistent.

(i) 3x + y – 2 = 0, kx + 2y – 3 = 0 and 2x – y = 3

By using determinant, show that the following points are collinear.
P(5, 0), Q(10, -3), R(-5, 6)

Find the value of k, if the area of the triangle with vertices at A(k, 3), B(-5, 7), C(-1, 4) is 4 square units.

Find k, if the following equations are consistent.

(ii) (k – 2)x + (k – 1)y = 17, (k – 1)x + (k – 2)y = 18, x + y = 5

Find k, if the following equations are consistent.

(i) x + 3y + 2 = 0, 2x + 4y – k = 0, x – 2y – 3k = 0