Formation and Graphical Solution of Linear Equations
Video Explanation
Question
Champa went to a sale to purchase some pants and skirts. She said that the number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased. Find how many pants and skirts Champa bought.
Solution
Step 1: Let the Variables Be
Let the number of pants = \(x\)
Let the number of skirts = \(y\)
Step 2: Form the Pair of Linear Equations
Skirts are two less than twice the number of pants:
\[ y = 2x – 2 \]
Skirts are four less than four times the number of pants:
\[ y = 4x – 4 \]
Step 3: Prepare Tables of Values
For Equation (1): \(y = 2x – 2\)
| x | y |
|---|---|
| 2 | 2 |
| 3 | 4 |
For Equation (2): \(y = 4x – 4\)
| x | y |
|---|---|
| 2 | 4 |
| 3 | 8 |
Step 4: Graphical Representation
Plot the following points on the same Cartesian plane:
- Line 1: (2, 2) and (3, 4)
- Line 2: (2, 4) and (3, 8)
Join each pair of points to obtain two straight lines.
The two straight lines intersect at the point (1, 0).
Result
From the graph, the solution of the given system of equations is:
\[ x = 1,\quad y = 0 \]
Answer
Number of pants purchased = 1
Number of skirts purchased = 0
Conclusion
Therefore, Champa bought 1 pant and no skirt.