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Question
Solve graphically, the following equations.
x + 2y = 4; 3x - 2y = 4.
Take 2 cm = 1 unit on each axis.
Also, find the area of the triangle formed by the lines and the x-axis.
Solution
x + 2y = 4
⇒ x = 4 - 2y
The table of x + 2y = 4 is
| X | 2 | - 4 | 12 |
| Y | 1 | 4 | - 4 |
3x - 2y = 4
⇒ x = `(4 + 2y)/(3)`
The table of 3x - 2y = 4 is
| X | 2 | 4 | 6 |
| Y | 1 | 4 | 7 |
Now plotting the points on a graph and we get the following required graph:
Therefore the solution of the given system of equations is (2,1).
Thus the vertices of the triangle are:
A(2,1), B`(4/3,0)`and C(4,0)
AB ⊥ BC and D ≡ (2,0)
AD = 1 and BC = `2(2)/(3) "units" = (8)/(3) "units"`
Area of the triangle ABC = `(1)/(2) xx "AD" xx "BC"`
= `(1)/(2) xx 1 xx (8)/(3)`
= `(4)/(3)"sq.units"`
= `1(1)/(3)"sq.units"`
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