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Class 10 › Mathematics › Pair of Linear Equations in Two Variables
CBSE2026Class Class 10 · Mathematics3 Marks · Short✅ Verified
(a) Solve the following pair of linear equations: 31x + 43y - 117 = 0; 43x + 31y = 105
OR
(b) When 1 is subtracted from the numerator and 2 is added to the denominator of a fraction, it becomes 1/2. When 7 is subtracted from the numerator and 2 is subtracted from the denominator, the fraction becomes 1/3. Find the fraction.
✅ Answer & Solution
**(a)** $31x+43y=117$ ...(i); $43x+31y=105$ ...(ii)
Adding (i) & (ii): $74x+74y=222 \Rightarrow x+y=3$ ...(iii)
Subtracting (ii) from (i): $-12x+12y=12 \Rightarrow y-x=1$ ...(iv)
Adding (iii) and (iv): $2y=4 \Rightarrow y=2$, then $x=1$.
**Answer: x = 1, y = 2**
**(b)** Let fraction $=\frac{x}{y}$.
$\frac{x-1}{y+2}=\frac12 \Rightarrow 2x-y=4$ ...(i)
$\frac{x-7}{y-2}=\frac13 \Rightarrow 3x-y=19$ ...(ii)
Subtracting (i) from (ii): $x=15$. From (i): $y=2(15)-4=26$.
**Fraction $=\frac{15}{26}$**
