#### Solve simultaneous linear equations:

(i) 3x + 14y = 5xy

21y – x = 2xy

(ii) 3x + 5y = 4xy

2y – x = xy.

**Solution:**

(i) 3x + 14y = 5xy

21y – x = 2xy

Now dividing each equation by xy of x ≠ 0, y ≠ 0

3x/xy + 14y/xy = 5xy/xy

By further calculation

3/y = 14/x = 5 ….. (1)

(ii) 3x + 5y = 4x

2y – x = xy

We can write it as

3x + 5y = 4xy

– x + 2y = xy

Divide each equation by xy if x≠ 0 and y ≠ 0

3x/xy + 5y/xy = 4xy/xy

So we get

3/y + 5/x = 4 ….. (1)

-x/xy + 2y/xy = xy/xy

So we get

-1/y + 2/x = 1 ….. (2)

Now multiply equation (1) by 1 and (2) by 3

3/y + 5/x = 4

-3/y + 6/x = 3

By adding both the equations

11/x = 7

So we get

x = 11/7

Substitute the value of x in equation (2)

-1/y + 2/11/7 = 1

By further calculation

-1/y + (2 × 7)/ 11 = 1

-1/y + 14/11 = 1

We can write it as

-1/y = 1 – 14/11

Taking LCM

-1/y = (11 – 14)/ 11

So we get

-1/y = -3/11

By cross multiplication

-3y = – 11

y = – 11/-3 = 11/3

Therefore, x = 11/7 and y = 11/3.

**More Solutions:**

- Solve simultaneous linear equations: (i) 2a(2)x – bx + 2a(2) – b
- Solve simultaneous linear equations: (i) (x2 – y2)z + (y2 – z2)x
- Solve simultaneous linear equations: (i) b(c -d)2 + a(d – c) + 3c – 3d
- Solve simultaneous linear equations: (i) x(x + z) – y (y + z)
- Solve simultaneous linear equations: (i) 9×2 + 12x + 4 – 16y2
- Solve simultaneous linear equations: (i) 21×2 – 59xy + 40y2
- Solve simultaneous linear equations: (i) x2y2 – xy – 72
- Solve simultaneous linear equations: (i) (3a – 2b)2 + 3(3a – 2b) – 10
- Solve simultaneous linear equations: (i) (x2 – x) (4×2 – 4x – 5) – 6