Solve the following pair of equations graphically: 2x+3y+4=0 2x−3y−8=0  Also, find the area of the region formed by the lines with the x -axis.

# Solve the following pair of equations graphically:Also, find the area of the region formed by the lines with the x -axis.

1. A
x = 6, y = 0 and Area =
2. B
x = 0, y = 6 and Area =
3. C
x = 1, y = -2 and Area =
4. D
x = -2, y = 1 and Area =

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### Solution:

We have been given two equations:   and  . We need to draw the graphs of these equations and further calculate the area bounded by these lines and x-axis.
We have,

Now constructing value table based on equation (i), we have,
Similarly, we have,

Now constructing value table based on equation (ii), we have,
Now, based on these two tables, the graph constructed is:
From the graph we can observe that both of the lines intersect at  , therefore the values of x and y will be 1 and -2.
The area bounded by these lines and x-axis is in a shape of triangle.
Area of triangle is given as: Area $\left(∆\mathit{ABC}\right)=\frac{1}{2}\left(\mathit{base}\right)\left(\mathit{height}\right)$.
From graph, we have,
Base = 6 units
Height = 2 units
Since, the measurements cannot be negative, we have taken base as positive.
Therefore, the area is given by:
Area =
Area =
Area =  .
Hence, the area of region bounded by the lines and x-axis is  .
Therefore, option 3 is correct.

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