Question

Solve for x and y:

7(y + 3) – 2(x + 2) = 14, 4(y – 2) + 3(x – 3) = 2

Answer 1

The given equations are:

7(y + 3) – 2(x + 2) = 14

⇒ 7y + 21 – 2x – 4 = 14

⇒ –2x + 7y = –3   ...(i)

And 4(y – 2) + 3(x – 3) = 2

⇒ 4y – 8 + 3x – 9 = 2

⇒ 3x + 4y = 19   ...(ii)

On multiplying (i) by 4 and (ii) by 7, we get:

–8x + 28y = –12  ...(iii)

21x + 28y = 133  ...(iv)

On subtracting (iii) from (iv), we get:

29x = 145

⇒ x = 5

On substituting x = 5 in (i), we get:

–10 + 7y = –3

⇒ 7y = (–3 + 10)

⇒ 7y = 7

⇒ y = 1

Hence, the solution is x = 5 and y = 1.