If 2x - 3y = -11 and 3x + 2y = 3, evaluate \( (y

Explanation

2x - 3y = -11 --- (i)

3x + 2y = 3 --- (ii)

Multiply equation (i) by 3 and equation (ii) by 2

6x - 9y = -33 --- (iii)

6x + 4y = 6 --- (iv)

Subtract equation (iii) from (iv)

13y = 39

y = \(\frac{39}{13}\) = 3

substitute (3) for y in equation (ii)

3x + 2(3) = 3

3x + 6 = 3

3x = 3 - 6

3x = -3

x = \(\frac{-3}{3}\) = - 1

Now,

\((y - x)^2 = (3 - (-1))^2\)

= \((3 + 1)^2\)

= \(4^2\)

= 16