Draw the graphs of the lines x - y = 1 and 2x + y = 8. Shade the area formed by these two lines and the y - axis. Also, find this area.

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Solution

i) x - y = 1

y = x - 1

x

0

1

2

3

y

-1

0

1

2

(ii) 2x + y = 8

y = 8 - 2x

x

0

1

2

4

y

8

6

4

0

The two lines intersect at point (3, 2). So, the solution of the given pair of linear equations is x = 3, y = 2.

Area of the required region (triangle)= $\frac{1}{2} \times b a s e \times h e i g h t = \frac{1}{2} \times 9 \times 3 = 13.5$

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Draw the graphs of the lines x - y = 1 and 2x + y = 8. Shade the area formed by these two lines and the y - axis. Also, find this area.

i) x - y = 1 y = x - 1 x 0 1 2 3 y -1 0 1 2 (ii) 2x + y = 8 y = 8 - 2x x 0 1 2 4 y 8 6 4 0 The two lines intersect at point (3, 2). So, the solution of the given pair of linear equations is x = 3, y = 2. Area of the required region (triangle)=12×base×height=12×9×3=13.5