Subtract the sum of 2x − 7y – 1 and −6x + 3y + 9 from the sum of 5x + 7y − 12 and 3x − 5y + 2.

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Solution

Sum of 5x + 7y – 12 and 3x – 5y + 2.

= 5x + 7y – 12 + 3x – 5y + 2

= (5x + 3x) + (7y – 5y) + (– 12 + 2)

= 8x + 2y – 10.

Again Sum of 2x – 7y – 1 and – 6x + 3y + 9

= 2x – 7y – 1 + (– 6x) + 3y + 9

= 2x – 7y – 1 – 6x + 3y + 9

= (2x – 6x) + (– 7y + 3y) + (– 1 + 9)

= (– 4x) + (– 4y) + 8

= - 4x - 4y – 8

Now

8x + 2y – 10 – (– 4x – 4y + 8)

= 8x + 2y – 10 + 4x + 4y – 8

= (8x + 4x) + (2y + 4y) + (– 10 + (– 8))

= 12x + 6y + (– 10 – 8)

= 12x + 6y + (-18)

= 12x + 6y -18

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