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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. - Algebra

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.

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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

  Is there an error in this question or solution?
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