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) = 7
⇒y = 1
Hence, the solution is x = 5 and y = 1.