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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 6 · Set 1 · Q21
(a) Solve the following pair of equations algebraically: 101 x+102 y=304; 102 x+101 y=305
(a)
Solve the following pair of equations algebraically : \[\begin{aligned} & 101 x+102 y=304 \\ & 102 x+101 y=305 \end{aligned} \]
OR
(b)
In a pair of supplementary angles, the greater angle exceeds the smaller by $\displaystyle 50$°. Express the given situation as a system of linear equations in two variables and hence obtain the measure of each angle.
Marking-scheme solution
(a)
Adding equations we get
\[x+y=3
\]
Subtracting equations we get
\[-x+y=-1
\]
Solving to get
\[x=2 \text { and } y=1
\]
OR
(b)
Let smaller angle be \(\displaystyle x\) and greater angle be y
\[\text { ATQ, } x+y=180
\]
Also \(\displaystyle y=x+50\)
Solving we get
\[x=65^{\circ} \text { and } \mathrm{y}=115^{\circ}
\]
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