Check whether the pair of equations $x-2y=0$ and $3x+4y=20$ is consistent; if so, solve it.
Step-by-Step Solution
Key Concept: Compare ratios to check consistency, then solve by substitution.
$\dfrac{a_1}{a_2}=\dfrac13,\ \dfrac{b_1}{b_2}=\dfrac{-2}{4}=-\dfrac12$; since these are unequal, the pair is consistent with a unique solution. [1.0 Mark]
From $x-2y=0$, $x=2y$. Substituting into $3x+4y=20$: $3(2y)+4y=20\Rightarrow 10y=20\Rightarrow y=2$. [1.0 Mark]
$x=2(2)=4$. So $x=4,\ y=2$. [1.0 Mark]
Correct Answer: