If the system of equations 4x – 5y = 6 and -12x + ay = b is inconsis

1.	If the system of equations 4x – 5y = 6 and -12x + ay = b is inconsistent. Which of the following cannot be the value of b? A) -20 B) -9 C) -7 D) -18
Answer» Correct option is (D) -18 Given that following system of equations is inconsistent. 4x – 5y = 6 ____________(1) and -12x + ay = b ____________(2) Condition for system of equations is inconsistent is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\) \(\Rightarrow\) \(\frac{4}{-12}=\frac{-5}{a}\neq\frac6b\) \(\Rightarrow\) \(\frac6b\neq\frac{4}{-12}\) \(\Rightarrow\) \(\frac6b\neq\frac{-1}3\) \(\Rightarrow\) \(b\neq6\times-3\) \(\Rightarrow\) \(b\neq-18\) Hence, if \(b\neq-18\) then given system is inconsistent. Hence, if given system is inconsistent then the value of b cannot be -18. Correct option is D) -18

If the system of equations 4x – 5y = 6 and -12x + ay = b is inconsistent. Which of the following cannot be the value of b? A) -20 B) -9 C) -7 D) -18

Answer»

Correct option is (D) -18

Given that following system of equations is inconsistent.

4x – 5y = 6 ____________(1)

and -12x + ay = b ____________(2)

Condition for system of equations is inconsistent is

\(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\)

\(\Rightarrow\) \(\frac{4}{-12}=\frac{-5}{a}\neq\frac6b\)

\(\Rightarrow\) \(\frac6b\neq\frac{4}{-12}\)

\(\Rightarrow\) \(\frac6b\neq\frac{-1}3\)

\(\Rightarrow\) \(b\neq6\times-3\)

\(\Rightarrow\) \(b\neq-18\)

Hence, if \(b\neq-18\) then given system is inconsistent.

Hence, if given system is inconsistent then the value of b cannot be -18.

Correct option is D) -18