Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Pair of Linear Equations in Two Variables

Short Answer Type

181. Check, whether, x = 5 and y = —2 is a solution of the system of simultaneous linear equations 2x + 3y = 4 and 3x + 5y = 5. Also state whether system is consistent or inconsistent.

109 Views

182. Check whether, x = 4, y = 5 and x = 2, y = 7.5 are solutions of the system of equation

straight x over 2 plus straight y over 5 equals 3

nd 10x + 4y = 50. Also, state, whether system is consistent or inconsistent.

111 Views

183. Tanvika goes to Monday market with her brother Nimit to have “Gol-gappa” and “dahi-bhalla”. They took number of plates of “gol-gappa” twice that of “dahi-bhalla”. The cost of one plate of gol-gappa was Rs. 5 and cost of one plate of dahi-bhalla was Rs. 10. They spent Rs. 60 which they had spent for market. Represent the situation algebraically.

116 Views

184. Pankaj Jain is three times as old as his son. In 12 years time, he will twice as old as his son. Represent the situation algebraically.

109 Views

185. Romila went to a stationary shop and purchased 2 pencils and 3 erasers for Rs 9. Her friend Sonali saw the new variety of pencils and erasers with Romila and she also bought 4 pencils and 6 erasers of the same kind for Rs. 18. Represent the situation algebraically.

840 Views

186. If x = 2, y = 4, find the value of p when 7x - 4y = p.

101 Views

187. Manish says to Rahim “I am three times as old as you are.” Later Manish says to Rahim “After 5 years I shall be two times as old as you will be.” Represent this situation algebraically and graphically.

Let present age of Manish be x years and present age of Rahim be y years.
Case I. x = 3y
⇒ x - 3y = 0
Case II.
After 5 years :
Age of Manish = (x + 5) years
Age of Rahim = {y + 5) year

Fig. 3.18.
According to question
x + 5 = 2(y + 5)
⇒    x + 5 = 2y + 10
⇒    x - 2y = 10 - 5
⇒    x - 2y = 5
So, algebraic representation be
x - 3y = 0    ...(i)
x - 2y = 5    ...(ii)
Graphical representation
For eqn. (i), we have
x - 3y = 0
⇒    x = 3y
Thus, we have following table :

For eqn. (ii), we have
x - 2y = 5
⇒ x = 5 + 2y
Thus, we have following tables :

When we plot the graph of the equation, we find that both the lines intersect at one point.
Hence, given system of equations has a unique solution.
So, we can say that system is consistent.

462 Views