Question

solve 31x+29 y=33 , 29x+31y=27

Answer 1

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Answer 2

The given equations are

31x + 29y = 33 ..... (1)

29x + 31y = 27 ..... (2)

Using substitution method.

From (1), we get

y = (33 - 31x)/29

Substituting y = (33 - 31x)/29 in (2), we get

29x + 31 (33 - 31x)/29 = 27

or, (29 * 29 - 31 * 31) x + 31 * 33 = 27 * 29

or, (31² - 29²) x = 33 * 31 - 29 * 27

or, 120x = 240

or, x = 2

Then y = (33 - 31 * 2)/29 = - 1

Therefore the required solution is

x = 2, y = - 1

Another method.

Adding (1) and (2), we get

x + y = 1

or, y = 1 - x

From (1), we get

31x + 29 (1 - x) = 33

or, 31x + 29 - 29x = 33

or, 2x = 4

or, x = 2

Then y = 1 - 2 = - 1

Therefore the required solution is

x = 2, y = - 1