# NCERT Mathematics Class 10 Exemplar Ch 3 Pair of Linear Equations in Two Variables Part 5

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9. Solve the following pairs of equations:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

Answer: (i) (ii) (iii)

(iv) (v) (vi)

(vii)

10. Find the solution of the pair of equations and Hence, find λ, if

Answer:

11. By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them.

(i)

(ii)

(iii)

Answer: (i) consistent; , (ii) inconsistent

(iii) consistent. The solution is given by , where x can take any value, i.e., there are infinitely many solutions.

12. Draw the graph of the pair of equations and Write the vertices of the triangle formed by these lines and the y-axis. Also find the area of this triangle.

Answer: sq. units.

13. Write an equation of a line passing through the point representing solution of the pair of linear equations and . How many such lines can we find?

Answer: ; Infinitely many lines.

14. If is a factor of , then find the values of a and b given that .

Answer: , .

15. The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. Find x and y.

Answer:

16. Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?

Answer: Salim’s age = 38 years, Daughter’s age = 14 years.