Question

If the system of linear equation x - 4y + 7z = g, 3y - 5z = h, -2x + 5y - 9z = k is consistent, then:
(A) g + h + k = 0 (B) 2g + h + k = 0
(C) g + h + 2k = 0 (D) g + 2h + k = 0

Answer 1

It is given that the system of linear equations are

x-4y+7z- g =0

3y-5z-h=0

-2x+5y-9z-k=0.

and they are consistent.

• For a system of linear consistent equations the determinant of the augmented coefficient of matrix is zero.

• The equations are written in a matrix.

• They are simplified by row transformations.

• Finally cross multiplication is done

• We arrive at the relation given by 2g+h+k =0.