#### Solve the following systems of simultaneous linear equations by cross-multiplication method:

(i) 3x + 2y = 4

8x + 5y = 9

(ii) 3x – 7y + 10 = 0

y – 2x = 3.

**Solution:**

(i) 3x + 2y = 4

8x + 5y = 9

We can write it as

3x + 2y – 4 = 0

8x + 4y – 9 = 0

By cross multiplication method

x/ (-18 + 20) = y/ (-32 + 27) = 1/ (15 – 16)

By further calculation

x/2 = y/-5 = 1/-1

So we get

x/2 = – 1

x = – 2

y = – 5 (-1) = 5

Therefore, x = – 2 and y = 5.

(ii) 3x – 7y + 10 = 0

y – 2x = 3

We can write it as

3x – 7y + 10 = 0

y – 2x – 3 = 0

By cross multiplication method

x/ (21 – 10) = y/ (-20 + 9) = 1/ (3 – 14)

By further calculation

x/11 = y/-11 = 1/-11

So we get

x/11 = 1/-11

x = – 1

Similarly

y/-11 = 1/ -11

y = 1

Therefore, x = – 1 and y = 1.

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