Solve the following simultaneous equation. 12x+17y=53;17x+12y=63 .

Solve the following simultaneous equation. $12 x + 17 y = 53; 17 x + 12 y = 63$ .

A
$x = 3, y = 1$
B
$x = 2, y = 1$
C
$x = 1, y = 1$
D
$x = 9, y = 1$

Solution:

Given equations are

12 x + 17 y = 53

...(1)

17 x + 12 y = 63

...(2)
On adding equations (1) and (2), we get,

29 x + 29 y = 116

\Rightarrow x + y = 4

....(3)
On subtracting equation (1) from equation(2), we get,

5 x - 5 y = 10

\Rightarrow x - y = 2

....(4)
On adding equations (3) and (4), we get,

2 x = 6

\Rightarrow x = 3

By putting

x = 3

in equation (3), we get,
⇒

3 + y = 4

\Rightarrow y = 1

Hence, the correct option is 1.

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