a piggy bank collection consisted of coins of Rs.2 and Rs.5. In all there were 77 coins totaling Rs.220. Write a pair of linear equations in two variables x and y to represent the above information

Let:
- \( x \) represent the number of Rs.2 coins.
- \( y \) represent the number of Rs.5 coins.

### Given:
- The total number of coins is 77.
- The total value of all the coins is Rs.220.

### Linear equations:
1. The total number of coins equation:
   \[
   x + y = 77
   \]
2. The total value of the coins equation:
   \[
   2x + 5y = 220
   \]

So, the pair of linear equations is:
\[
\begin{aligned}
x + y &= 77 \\
2x + 5y &= 220
\end{aligned}
\]

Would you like further details on solving this system of equations or clarifications?

Here are 5 related questions:
1. How do you solve these equations using substitution?
2. How do you solve these equations using elimination?
3. What is the meaning of the solution in the context of this problem?
4. How can the graph of these equations be used to find the solution?
5. How would the equations change if the total value was Rs.300 instead of Rs.220?

**Tip:** When solving linear equations, substitution and elimination methods are both effective. Try both to gain deeper understanding.

A piggy bank collection consisted of coins of Rs.2 and Rs.5. In all there were 77 coins totaling Rs.220. Write a pair of linear equations in two variables x and y to represent the above information.

Learn how to represent a collection of Rs.2 and Rs.5 coins in a piggy bank using linear equations. This example uses a total of 77 coins and a combined value of Rs.220. Understand the step-by-step solution, including the formulation of the system of equations. Suitable for students in Grades 8-10.

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