Question

Solve the following pair of simultaneous equations.

`5/x - 3y = 7, 3/x - 2y = 4`

Answer 1

Given equations:

`5/x - 3y = 7`     ...(1)

`3/x - 2y = 4`     ...(2)

Let, z = `1/x`

Then the equations will become:

5z − 3y = 7     ...(1)

3z − 2y = 4     ...(2)

Here, multiplying equation (1) by 2:

2(5z) + 2(3y) = 2(7)

9z − 6y = 12     ...(3)

And, multiplying equation (2) by 3:

3(3z) + 3(2y) = 3(4)

10z − 6y = 14    ...(4)

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

(10z − 6y) − (9z − 6y) = 14 − 12

10z − 6y − 9z + 6y = 2

10z − 9z = 2

∴ z = 2

Let’s substitute z = 2 into equation (2):

3(2) − 2y = 4

6 − 2y = 4

−2y = 4 − 6

−2y = −2

y = `(-2)/(-2)`

∴ y = 1

Thus, finding x from z = `1/x`

`1/x` = 2

∴ x = `1/2`