If 2x - 3y = -11 and 3x + 2y = 3, evaluate \( (y - x)^2\)
A.
16
B.
25
C.
9
D.
4
Correct answer is A
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
