Solve the linear equation

31x + 29y = 33

29x + 31y = 27

x = 2

y = - 1

Step-by-step explanation:

Make the coefficient of x the same

Multiply the first equation by 29

31x + 29y = 33 becomes

899x + 841y = 957

Multiply the second equation by 31

29x + 31y = 27 becomes

899x + 961y = 837

Subtract the equations

(899x + 841y) - (899x + 961y) = 957 - 837

(899x - 899x) + (841y - 961y) = 120

841y - 961y = 120

-120y = 120

y = 120/-120 = - 1

Substitute the value of y into both equations to find the value of x and check its right.

31x + 29y = 33

31x + 29 (-1) = 33

31x - 29 = 33

31x = 33 + 29

31x = 62

x = 62/31 = 2

29x + 31y = 27

29x + 31 (-1) = 27

29x - 31 = 27

29x = 27 + 31

29x = 58

x = 58/29 = 2