Question

Consider set of linear equations :$Qx+18y=27$ and $9y=12x+72$, Where $Q$ is a constant and no ordered pair satisfies both the equation simultaneously. Then, What will be the value of $Q$?

• A. $Q=20$
• B. $Q=-24$
• C. $Q=24$
• D. $Q=30$

Answer 1

The correct option is B $Q=-24$

Given,
$Qx+18y=27$
$9y=12x+72$

Given: No ordered pair satisfies both the equation simultaneously.

Hence, the system of simultaneous equations have No solution.

Concept: For no solution, slope of both equations must be same.

Now, converting both equations in slope intercept form.
$Qx+18y=27\Rightarrow 18y=-Qx+27\Rightarrow y=\frac{-Q}{18}x+\frac{27}{18}\text{Slope}=\frac{-Q}{18}$.


$9y=12x+72\Rightarrow y=\frac{12}{9}x+\frac{72}{9}\text{Slope}=\frac{12}{9}=\frac{4}{3}$

Now, equating both the slope we get,
$\frac{-Q}{18}=\frac{4}{3}$
On simplifying we get,
$Q=-24.$