# Draw the Graphs of the Linear Equations 4x − 3y + 4 = 0 and 4x + 3y − 20 = 0. Find the Area Bounded by These Lines and X-axis. - Mathematics

Draw the graphs of the linear equations 4x − 3y + 4 = 0 and 4x + 3y − 20 = 0. Find the area
bounded by these lines and x-axis.

#### Solution

We have

4x - 3y +  4 = 0

⇒  4x - 3y = 4

⇒  x = ( 3y  - 4 ) / 4

Putting   y = 0 . we get  ( 3 xx 0 - 4) / 4  = -1

Putting  y  = 4 , we get  ( 3 xx 4- 4) / 4  = - 2

Thus, we have the following table for the p table for the points on the line   4x - 3y  + 4 = 0

 x - 1 2 y 0 4

we have

4x + 3y - 20 = 0

⇒   4x = 20 - 3y

⇒  x = ( 20 - 3y )/ 4

Putting  y = 0 , we get   x  = (20 - 3 xx 0) /4 = 5

Puttiing  y = 4  , we get  x = ( 20 - 3 xx 4 ) / 4 = 2

Thus, we have the following table for the p table for the points on the line 4x  - 3y - 20 = 0

 x 0 2 y 0 4

\

Clearly, two lines intersect at A ( 2 , 4 )
The graph of the lines  4x - 3y + 4 = 0   and  4x  + 3y - 20 = 0  intersect with y - axis at
a + B (- 1 , 0 ) and  c ( 5 , 0 )respectively

∴ Area of Δ ABC  = 1/ 2  [  Base xx height ]

= 1 / 2  ( BC xx AB )

= 1 / 2  ( 6 xx 4)

=  3 xx 4

12 sq .units

∴ Area of Δ ABC  = 12 sq .units

Concept: Equations of Lines Parallel to the X-axis and Y-axis
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 7 Linear Equations in Two Variables
Exercise 7.3 | Q 18

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