Formation and Graphical Solution of Linear Equations
Video Explanation
Question
10 students of class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
Solution
Step 1: Let the Variables Be
Let the number of boys = \(x\)
Let the number of girls = \(y\)
Step 2: Form the Linear Equations
Total number of students = 10
\[ x + y = 10 \quad \text{(Equation 1)} \]
Number of girls is 4 more than number of boys
\[ y = x + 4 \quad \text{(Equation 2)} \]
Step 3: Prepare Tables of Values
For Equation (1): \(x + y = 10\)
| x | y |
|---|---|
| 4 | 6 |
| 6 | 4 |
For Equation (2): \(y = x + 4\)
| x | y |
|---|---|
| 2 | 6 |
| 4 | 8 |
Step 4: Graphical Representation
Plot the following points on the same Cartesian plane:
- Line 1: (4, 6) and (6, 4)
- Line 2: (2, 6) and (4, 8)
Join each pair of points to obtain two straight lines.
The two straight lines intersect at the point (3, 7).
Result
From the graph, the solution of the given system of equations is:
\[ x = 3,\quad y = 7 \]
Answer
Number of boys = 3
Number of girls = 7
Conclusion
Therefore, 3 boys and 7 girls took part in the Mathematics quiz.