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Question

Solve the following system of equations graphically.

2x − 3y + 6 = 0
2x + 3y − 18 = 0

Also, find the area of the region bounded by these two lines and y-axis.

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Solution

The given equations are:

Putting in equation (i) we get:

Putting in equation (i) we get:

Use the following table to draw the graph

Draw the graph by plotting the two points from table.

Putting in equationwe get:

Putting in equationwe get:

Use the following table to draw the graph.

Draw the graph by plotting the two points from table.

The two lines intersect at.

Hence is the solution of the given equations.

The area enclosed by the lines represented by the given equations and the y−axis

Now,

Required area = Area of PCA

Required area =

Required area =

Required area =

Hence the required area is


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