#### Solve simultaneous linear equations:

(i) 3x + 4y = 10

2x – 2y = 2

(ii) 2x = 5y + 4

3x – 2y + 16 = 0

**Solution:**

(i) 3x + 4y = 10 ….. (1)

2x – 2y = 2 ….. (2)

Multiplying equation (1) by 1 and (2) by 2

3x + 4y = 10

4x – 4y = 4

By adding both the equations

7x = 14

By division

x = 14/7 = 2

Substituting the value of x in equation (2)

2 × 2 – 2y = 2

By further calculation

4 – 2y = 2

So we get

2y = 4 – 2 = 2

y = 2/2 = 1

Therefore, x = 2 and y = 1.

(ii) 2x = 5y + 4

3x – 2y + 16 = 0

We can write it as

2x – 5y = 4 …. (1)

3x – 2y = – 16 ….. (2)

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

6x – 15y = 12 ….. (3)

6x – 4y = – 32 ….. (4)

By subtracting both the equations

– 11y = 44

y = -44/11 = – 4

Substitute the value of y in equation (1)

2x – 5 (-4) = 4

By further calculation

2x + 20 = 4

So we get

2x = 4 – 20 = – 16

x = – 16/2 = – 8

Therefore, x = – 8 and y = – 4.

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