Question

For what value of a, if any, will the following system of equations in x, y and z have a
solution?
2x + 3y = 4, x + y + z = 4, x + 2y – z = a
(a) Any real number     (b) 0
(c) 1       (d) There is no such value

Answer 1

2x + 3y = 4 ........................(1)
x + y + z = 4 .....................(2)
x + 2y – z = a  ...................(3)

add (2) and (3),
x + y + z + x + 2y – z =  4 + a
2x + 3y = 4 + a ..................(4)

from (1) and (4),
value of a must be 0 otherwise no solution..

u may use matrix rank method for this ..

Answer 2

no solution exist therefore option   D

Comments

How?!!!