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Mathematics · 2024 · 2 marks
CBSE 2024 · Region 3 · Set 1 · Q22
(a) If 2 x+ y =13 and 4 x- y =17, find the value of (x- y ).
(a)
If $\displaystyle 2 x+\mathrm{y}=13$ and $\displaystyle 4 x-\mathrm{y}=17$, find the value of $\displaystyle (x-\mathrm{y})$.
OR
(b)
Sum of two numbers is $\displaystyle 105$ and their difference is 45. Find the numbers.
Marking-scheme solution
(a)
\[\begin{aligned}
& 2 x+y=13 \\
& 4 x-y=17
\end{aligned}
\]
Solving (i) and (ii)
\[\begin{aligned}
& x=5 \& y=3 \\
& x-y=2
\end{aligned}
\]
OR
(b)
Let the numbers be x, y (x > y)
\[x+y=105
\]
\[x-y=45
\]
on solving (i) and (ii)
\[\Rightarrow x=75 \quad \& \quad y=30
\]
∴ Numbers are $\displaystyle 75$, $\displaystyle 30$
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