Determinants Matrices Question 174
Question: The equations $ 2x+3y+4=0; $
$ 3x+4y+6=0 $ and $ 4x+5y+8=0 $ are
Options:
A) Consistent with unique solution
B) Inconsistent
C) Consistent with infinitely many solutions
D) None of the above
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] Consider first two equations: $ 2x+3y=-4 $ and $ 3x+4y=-6 $ We have $ \Delta = \begin{vmatrix} 2 & 3 \\ 3 & 4 \\ \end{vmatrix}=-1\ne 0 $
$ {\Delta _{x}}= \begin{vmatrix} -4 & 3 \\ -6 & 4 \\ \end{vmatrix}=2 $ and $ {\Delta _{y}}= \begin{vmatrix} 2 & -4 \\ 3 & -6 \\ \end{vmatrix}=0 $
$ \therefore x=-2 $ and $ y=0 $ Now this solution satisfies the third, so the equations are consistent with unique solution.
BETA
