Solve graphically 3x + y + 1 = 0 , 2x – 3y + 8 = 0 shade the area of region bounded by lines and x – axis
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Solve graphically
To find: the solution of 3x + y + 1 = 0, 2x - 3y + 8 = 0 graphically and to shade the area of region bounded by lines and x -axis
Solution:
Step 1. First equation
The equation is 3x + y + 1 = 0 or, y = - 3x - 1
- x : 0 || - 1
- y : - 1 || 2
- Using the points (0, - 1) and (- 1, 2), draw the line 3x + y + 1 = 0 on paper.
Step 2. Second equation
The equation is 2x - 3y + 8 = 0 or, y = (2x + 8)/3
- x : 2 || - 1
- y : 4 || 2
- Using the points (2, 4) and (- 1, 2), draw the line 2x - 3y + 8 = 0 on paper.
Step 3. Finding solution
- We see that the point (- 1, 2) lies on both the lines and thus it is their point of intersection.
- Therefore the required solution is
- x = - 1, y = 2 .
Step 4. Shading the bouded graph
We see that the region bounded by the given lines and the x-axis lies on the negative side of the x-axis.
[[ Refer to the given attachment for the graph ]]
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