Q. 293.8( 12 Votes )
Draw the graphs o
For equation, 2x + y = 2
First, take x = 0 and find the value of y.
Then, take y = 0 and find the value of x.
Now similarly solve for equation, 2x + y = 6
Plot the values in a graph and find the intersecting point for the solution.
Since, the line 2x + y = 6 cuts the line y - axis at A(0,6) and x - axis at B(3,0)
& the line 2x + y = 2 cuts the x - axis at C(1,0) and y - axis at D(0,2).
Thus, it is clear from the graph that ABCD forms a trapezium.
And the coordinates joining this trapezium are (0,6),(3,0),(1,0) and (0,2).
We can find the area of trapezium ABCD.
The formula to calculate area of a trapezium ABCD is:
Area(trap. ABCD) = Area(∆OAB) – Area(∆OCD)
= (1/2 × 3 × 6) – (1/2 × 1 × 2)
[∵ base(∆OAB) = 3 units & height(∆OAB) = 6 units
= 9 - 1 base(∆OCD) = 1 units & height(∆OCD) = 2units]
= 8 sq. units
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