Q1.
a) x = 1, y = -1
b) x = 1, y = 0
c) x = a, y = b
d) x = ab, y = -ab
e) x = 3, y = 5
f) x = a², y = b²
g) x = m + n, y = m - 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 ≠ 3 and α ≠ -6; No solution for α = -6; Infinitely many solutions for α = 3
Q5. The numbers are 7 and 13
Q6. Monthly incomes are Rs. 900 and Rs. 700
Q7. Initial salary is Rs. 3000, annual increment is Rs. 300
Q8. The number is 27
Q9. 4 days
Q10. Present age of the father is 45 years
Q11. Number of students in the class is 48
Q12. c = 6
Q13.
a) x = 3, y = 2
b) x = 2, y = 1
Q14. The solution region is the area where both inequalities x + y ≤ 5 and 2x - y + 2 ≥ 0 are satisfied, bounded by the lines x + y = 5 and 2x - y + 2 = 0, including the intersection point (1, 4).
Parent Tip: Review the logic above to help your child master the concept of linear equation in two variables worksheet.
