Question

Solve the following pair of simultaneous equations.

65x + 49y = 293, 49x + 65y = 277

Answer 1

Given equations:

65x + 49y = 293     ...(1)

49x + 65y = 277     ...(2)

Here, multiplying equation (1) by 49:

49(65x) + 49(49y) = 49(293)

3185x + 2401y = 14357     ...(3)

And, multiplying equation (2) by 65:

65(49x) + 65(65y) = 65(277)

3185x + 4225y = 18005     ...(4)

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

(3185x + 2401y) − (3185x + 4225y) = 14357 − 18005

3185x + 2401y − 3185x − 4225y = −3648

2401y − 4225y = −3648

−1824y = −3648

y = `(−3648)/(−1824)`

∴ y = 2

Let’s substitute y = 2 into equation (1):

65x + 49(2) = 293

65x + 98 = 293

65x = 293 − 98

65x = 195

x = `195/65`

∴ x = 3