CBSE 2025 · Region 6 · Set 1 · Q28 · 3 marks
Check whether the following pair of equations is consistent or not. If consistent, solve graphically \[\begin{aligned} & x+3 y=6 \\ & 3 y-2 x=-12 \end{aligned} \]
Marking-scheme solution
\[\begin{aligned}
& x+3 y=6 \\
& -2 x+3 y=-12 \\
& \frac{a_{1}}{a_{2}}=\frac{1}{-2} ; \frac{b_{1}}{b_{2}}=\frac{3}{3}=1
\end{aligned}
\]
\(\displaystyle \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}\) Hence the pair of equations is consistent.Solution is \(\displaystyle (6, 0)\) or \(\displaystyle x=6\) and \(\displaystyle y=0\)
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