Draw the graphs of the pair of linear equations $x - y + 2 = 0$ and $4 x - y - 4 = 0$ . Calculate the area of the triangle formed by the lines so drawn and the x-axis .

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Solution

The given linear equations are

x − y
+ 2 = 0 .....(i)

4
x − y
− 4 = 0 .....(ii)

For (i), we have
x 0 −2
y 2 0

For (ii), we have
x 0 1
y −4 0

The graph of the lines represented by the given equations is shown below:

The triangle thus obtained has the vertices A(2, 4), B(−2, 0) and D(1, 0).

∴ Area of triangle ADB

=(1/2)×3×4=6 square units

Thus, the area of the triangle formed by the given lines and the
x
-axis is 6 square units.

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Draw the graphs of the pair of linear equations x − y + 2 = 0 and 4x − y − 4 = 0 . Calculate the area of the triangle formed by the lines so drawn and the x-axis .

Draw the graphs of the pair of linear equations $x - y + 2 = 0$ and $4 x - y - 4 = 0$ . Calculate the area of the triangle formed by the lines so drawn and the x-axis .