Formation and Graphical Solution of Linear Equations
Video Explanation
Question
5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and one pen.
Solution
Step 1: Let the Variables Be
Let the cost of one pencil = \(x\) rupees
Let the cost of one pen = \(y\) rupees
Step 2: Form the Pair of Linear Equations
From the first condition:
\[ 5x + 7y = 50 \quad \text{(Equation 1)} \]
From the second condition:
\[ 7x + 5y = 46 \quad \text{(Equation 2)} \]
Step 3: Prepare Tables of Values
For Equation (1): \(5x + 7y = 50\)
| x | y |
|---|---|
| 3 | 5 |
| 1 | \(\frac{45}{7}\) |
For Equation (2): \(7x + 5y = 46\)
| x | y |
|---|---|
| 3 | 5 |
| 1 | \(\frac{39}{5}\) |
Step 4: Graphical Representation
Plot the following points on the same Cartesian plane:
- Line 1: (3, 5) and (1, 45/7)
- Line 2: (3, 5) and (1, 39/5)
Join each pair of points to obtain two straight lines.
The two straight lines intersect at the point (3, 5).
Result
From the graph, the solution of the given system of equations is:
\[ x = 3,\quad y = 5 \]
Answer
Cost of one pencil = Rs. 3
Cost of one pen = Rs. 5
Conclusion
Therefore, the cost of one pencil is Rs. 3 and the cost of one pen is Rs. 5.