Q. 2 D5.0( 1 Vote )

# By comparing the co-efficient of the same variables and constants of the following pairs of equations, let us write whether the pair of equations is solvable or not and check them by drawing the graphs of the equations.

3x + 2y = 6

12x + 8y = 24

Answer :

3x + 2y = 6 …(1)

12x + 8y = 24 …(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} ]

3x + 2y = 6 12x + 8y = 24

∴ 3x + 2y + (-6) = 0 ∴ 12x + 8y + (-24) = 0

Or 3 × x + 2 × y + (-6) = 0 or, 12 × x + 8 × y + (-24) = 0

Here a_{1} = 3, b_{1} = 2, c_{1} = -6 and a_{2} = 12, b_{2} = 8, c_{2} = -24

Comparing the ratio of , we get

, and

Here . Therefore, it is solvable and has infinite common solutions. Lines will overlap.

Now, plot the lines on graph,

3x + 2y = 6 y = ... equation (i)

Equation (i) will be plotted as line AB.

12x + 8y = 24 y = ... equation (ii)

Equation (ii) will be plotted as line CD.

Here in the graph also, we can see that both lines are overlapping on each other. Therefore it has infinite common solutions.

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