Question

STATEMENT - 1 :$\sqrt{2}x+\sqrt{3}y=0,\sqrt{3}x-\sqrt{8}y=0$ has no solution.
STATEMENT - 2 : If a pair of linear equations is given by $a_{1}x+b_{1}y+c_1=0,a_{2}x+b_{2}y+c_2=0$ and $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}\ne \frac{c_1}{c_2}$.
In this case, the pair of linear equations is consistent.

• A. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1
• B. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1
• C. Statement - 1 is True, Statement - 2 is False
• D. Statement - 1 is False, Statement - 2 is True

Answer 1

Answer: (D)

Statement - 1 is False, Statement - 2 is True

For equations $S_1:\frac{a_1}{a_2}\ne \frac{b_1}{b_2}\ne \frac{c_1}{c_2}$ and hence the pair of lines will be consistent and will have unique solution.
If $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}\ne \frac{c_1}{c_2}$, then there will be a unique solution and hence the system of equations will be consistent.