Question

Solve the following pair of simultaneous equations.

31x + 37y = 25, 37x + 31y = 43

Answer 1

Given equations:

31x + 37y = 25     ...(1)

37x + 31y = 43     ...(2)

Here, multiplying equation (1) by 37:

37(31x) + 37(37y) = 37(25)

1147x + 1369y = 925     ...(3)

And, multiplying equation (2) by 31:

31(37x) + 31(31y) = 31(43)

1147x + 961y = 1333     ...(4)

Now, subtracting equation (3) from equation (4):

(1147x + 1369y) − (1147x + 961y) = 925 − 1333

1147x + 1369y − 1147x − 961y = −408

1369y − 961y = −408

408y = −408

y = `(−408)/408`

∴ y = −1

Let’s substitute y = −1 into equation (1):

31x + 37(−1) = 25

31x − 37 = 25

31x = 25 + 37

31x = 62

x = `62/31`

∴ x = 2