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Question

Draw the graphs of the equations xy + 1 = 0 and 3x + 2y − 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.


Solution

xy + 1 = 0

x = y − 1

x

0

1

2

y

1

2

3

3x + 2y − 12 = 0

x

4

2

0

y

0

3

6

Hence, the graphic representation is as follows.

From the figure, it can be observed that these lines are intersecting each other at point (2, 3) and x-axis at (−1, 0) and (4, 0). Therefore, the vertices of the triangle are (2, 3), (−1, 0), and (4, 0).


Mathematics
Math
Standard X

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