#### Solve simultaneous linear equations:

(i) 15x – 14y = 117

14x – 15y = 115

(ii) 41x + 53y = 135

53x + 41y = 147.

**Solution:**

(i) 15x – 14y = 117 ….. (1)

14x – 15y = 115 ….. (2)

Now multiply equation (1) by 14 and (2) by 15

210x – 196y = 1638 …. (3)

210x – 225y = 1725 ….. (4)

By subtracting both the equations

29y = – 87

So we get

y = -87/29 = – 3

Substitute the value of y in equation (1)

15x – 14 (-3) = 117

By further calculation

15x + 42 = 117

So we get

15x = 117 – 42 = 75

By division

x = 75/15 = 5

Therefore, x = 5 and y = – 3.

(ii) 41x + 53y = 135 ….. (1)

53x + 41y = 147 ….. (2)

Now multiply equation (1) by 53 and (2) by 41

2173x + 2809y = 7155 ….. (3)

2173x + 1681y = 6027 ….. (4)

By subtracting both the equations

1128y = 1128

So we get

y = 1128/1128 = 1

Substitute the value of y in equation (1)

41x + 53 × 1 = 135

By further calculation

41x + 53 = 135

So we get

41x = 135 – 53 = 82

By division

x = 82/41 = 2

Therefore, x = 2 and y = 1.

**More Solutions:**

- Solve simultaneous linear equations: (i) x/6 = y – 6
- Solve simultaneous linear equations: (i) 9 – (x – 4) = y + 7
- Solve simultaneous linear equations: x – 3y = 3x – 1 = 2x – y.
- Solve simultaneous linear equations: (i) 4x + (x – y)/ 8 = 17
- Solve simultaneous linear equations: (i) 3/x + 4y = 7
- Solve simultaneous linear equations: (i) px + qy = p – q
- Solve 2x + y = 23, 4x – y = 19.
- The expression ax + by has value 7 when x = 2, y = 1.
- Can the following equations hold simultaneously?