Q. 3 A5.0( 4 Votes )

# Let us determine the relations of ratios of the same variable and constants of the following pairs of equations and write whether the graphs of the equations will be parallel or intersecting or overlapping.

5x + 3y = 11

2x – 7y = –12

Answer :

5x + 3y = 11 …(1)

2x – 7y = –12 …(2)

Let us express the equations (1) and (2) in the form of

ax + by +c = 0 where a and b can’t be 0 at the same time.

[In the first equation, we use a_{1}, b_{1}, c_{1} and in second equation, we use a_{2}, b_{2}, c_{2} ]

5x + 3y = 11 2x – 7y = –12

∴ 5x + 3y + (-11) = 0 ∴ 2x – 7y + 12 = 0

Or 5 × x + 3 × y + (-11) = 0 or, 2 × x + (-7) × y + 12 = 0

Here a_{1} = 5, b_{1} = 3, c_{1} = -11 and a_{2} = 2, b_{2} = -7, c_{2} = 12

Comparing the ratio of , we get

, and

Here . Therefore, it has one common solution. Graph of equations will intersect at a point.

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