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The path of highway number 1 is given by the equation x + y = 7 and the highway number 2 is given by the equation 5x + 2y = 20. Represent these equations geometrically - Mathematics

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Sum

The path of highway number 1 is given by the equation x + y = 7 and the highway number 2 is given by the equation 5x + 2y = 20. Represent these equations geometrically

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Solution

We have, x + y = 7

⇒ y = 7 – x ….(1)

In tabular form

x 1 4
y 6 3
points A B

and 5x + 2y = 20

`⇒ y = \frac { 20-5x }{ 2 } ….(2)`

In tabular form

x 2 4
y 5 0
points C D

Plot the points A (1, 6), B(4, 3) and join them to form a line AB.

Similarly, plot the points C(2, 5). D (4, 0) and join them to get a line CD. Clearly, the two lines intersect at the point C. Now, every point on the line AB gives us a solution of equation (1). Every point on CD gives us a solution of equation (2)

Concept: Graphical Method of Solution of a Pair of Linear Equations
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