Q1.
a) x = 1, y = -1
b) x = 1, y = 1
c) x = a + b, y = a - b
d) x = ab, y = -ab
e) x = 1, y = 3
f) x = a², y = b²
g) x = m, y = n
h) x = 2, y = 3 or x = 3, y = 2
i) x = a, y = b
j) x = 2a, y = 2b
Q2. Pairs with infinitely many solutions: 4x - 5y = 3 and 8x - 10y = 6; Pair with unique solution: 5x - 4y = 5
Q3. k = -1
Q4. Unique solution for α ≠ 6; No solution for α = 6; Infinitely many solutions for α = 6 (Note: This contradicts the no solution case; typically for α=6, equations are inconsistent unless identical)
Q5. The numbers are 7 and 13.
Q6. Monthly incomes are Rs. 1800 and Rs. 1400.
Q7. Initial salary is Rs. 3300, annual increment is Rs. 300.
Q8. The number is 27.
Q9. It will take 4 days.
Q10. Present age of the father is 45 years.
Q11. Number of students in the class is 48.
Q12. c = 4
Q13.
a) x = 3, y = 2
b) x = 2, y = 1
Q14. The region to be shaded is the area below the line 2x - y + 2 = 0 and above the line x + y = 5, including the lines themselves.
Parent Tip: Review the logic above to help your child master the concept of solving equations with two variables worksheet.
