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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-ordinates of the point of intersection of these lines and find the area of triangle formed by these lines and the X-axis.
Solution
The given simultaneous equations are 4x + 3y = 24 and 4x - 3y = -24.
4x+3y =24 …........(i)
y =(24−4x)/3
| x | 0 | 3 | 6 |
| y | 8 | 4 | 0 |
| (x,y) | (0,8) | (3,4) | (6,0) |
4x-3y =-24 …...........(ii)
y =(4𝑥+24)/3
| x | 0 | -3 | -6 |
| y | 8 | 4 | 0 |
| (x,y) | (0,8) | (-3,4) | (-6,0) |
From the graph A (-6, 0), B(0, 8) C (6, 0) and AC = 12 units.
Height = h= 8 units
Base = b = 12 units
Area of triangle=(1/2) x Base x Height
A(ΔABC)= (1/2) x 12 x8
A(ΔABC)=48 sq units
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