State whether the following equation are solvable:
$2 x + 3 y = 7$ and $6 x + 9 y = 11$ .

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Solution

Given the equations are $2 x + 3 y = 7$ .....(1) and $6 x + 9 y = 11$ ....(2).
If possible let the equations are solvable and the solution pair is $(x, y)$ .
Now, (2) $-$ $3 \times$ (1) gives
$0 = - 10$ .
Which is a contradiction.
So the given equations are not solvable.

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2 x + 3 y = 10

6 x + 9 y = 11

6 x + 3 y = 7 x y and 3 x + 9 y = 11 x y

P S

P (2, 2),

Q (6, - 1)

R (7, 3) .

(1, - 1)

P S

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