Question

Solve the following pair of simultaneous equations.

73x + 27y = 19, 27x + 73y = −119

Answer 1

Given equations:

73x + 27y = 19     ...(1)

27x + 73y = −119     ...(2)

Here, multiplying equation (1) by 73:

73(73x) + 73(27y) = 73(19)

5329x + 1971y = 1387     ...(3)

And, multiplying equation (2) by 27:

27(27x) + 27(73y) = 27(−119)

729x + 1971y = −3213     ...(4)

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

(5329x + 1971y) − (729x + 1971y) = 1387 − (−3213)

5329x + 1971y − 729x − 1971y = 1387 + 3213

5329x − 729x = 4600

4600x = 4600

x = `4600/4600`

∴ x = 1

Let’s substitute x = 1 into equation (1):

73(1) + 27y = 19

73 + 27y = 19

27y = 19 − 73

27y = −54

y = `(-54)/27`

∴ y = −2