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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 3 · Set 2 · Q35
(a) Solve the following system of equations graphically: 2 x +3 y =5,-3 x + y =-2
Solve the following system of equations graphically: \[2 \mathrm{x}+3 \mathrm{y}=5,-3 \mathrm{x}+\mathrm{y}=-2 \]
The sum of the digits of a $\displaystyle 2$-digit number is 11. The number obtained by interchanging its digits exceeds the given number by 9. To know the number :
(i)
form the linear equations representing the above situation.
(ii)
verify that the equations have a unique solution.
(iii)
solve the equations to get the given $\displaystyle 2$-digit number.
Marking-scheme solution
Correct solution \(\displaystyle \mathrm{x}=1\) and \(\displaystyle \mathrm{y}=1\)
Let the digit at unit's place be x and at ten's place be y.
The number is \(\displaystyle 10 \mathrm{y}+\mathrm{x}\)
(i)
As per given statements
\[\begin{gathered}
x+y=11 \text { --- (1) } \\
10 x+y=10 y+x+9 \\
\Rightarrow x-y=1 \text { --- (2) }
\end{gathered}
\]
(ii)
Here, \(\displaystyle \frac{a_{1}}{a_{2}}=\frac{1}{1}, \frac{b_{1}}{b_{2}}=\frac{1}{-1}\) or - $\displaystyle 1$
Since \(\displaystyle \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}\)
Therefore, system of equations have a unique solution.
(iii) Solving equations ($\displaystyle 1$) & ($\displaystyle 2$), we get
\[x=6 \text { and } y=5
\]
Therefore, given number is 56.
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CBSE Class 10 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.