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Question

Draw the graphs representing the equations 4x +3y=24 and 3y=4x + 24 on the same graph paper . Write the Co-ordinate of the point of intersection of these and find the area of the triangle formed by these lines and the X-axis.

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Solution

Sol. For 4x + 3y = 24,
x
0
3
6
y
8
4
0
(x , y)
(0, 8)
(3, 4)
(6, 0)
Put, x = 0, we get y = 8
Put x = 3 we get y = 4 and
put x = 6 we get y = 0
For 3y = 4x + 24 ,
x
- 6
-3
0
y
0
4
8
(x , y)
(-6, 0)
(-3, 4)
(0,8)
Put x = - 6 we get y = 0
Put x = -3 we get y = 4
Put x = 0 we get y = 8
Now, we have ∆ ABC,
With Base BC = 12 units, Height AO = 8 units,
We know that, A (∆ ABC) = ½ (Base) (Height)
A(∆ ABC) = ½ (BC)(AO)
A(∆ ABC) = ½ (12)(8)
A(∆ ABC) = 6 × 8
A(∆ ABC) = 48 sq. units.

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