Multivariable Calc Question? Help

https://eee.uci.edu/12z/44265/home/MidExam-sample.pdf

Question #1, I keep on getting 120 but the answer is 75/2. Can someone please help?

Are you sure about the answer?
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The boundaries of R suggests the substitution
u = y - 2x and v = y + 4x.
<==> x = (u - v)/(-6) and y = (2u + v)/3.

So, R transforms to u in [-2, 3] and v in [1, 3].

Moreover, the Jacobian ∂(u,v)/∂(x,y) equals
|-2 1|
|4 1| = -6.

Hence, |∂(x,y)/∂(u,v)| = |1/(-6)| = 1/6.
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So, change of variables yields
∫∫R (4x + y) dA
= ∫(u = -2 to 3) ∫(v = 1 to 3) [4(u - v)/(-6) + (2u + v)/3] * (1/6) dv du
= (1/18) ∫(u = -2 to 3) ∫(v = 1 to 3) 3v dv du
= (1/18) ∫(u = -2 to 3) (3/2) v^2 {for v = 1 to 3} du
= (1/18) ∫(u = -2 to 3) 12 du
= (12/18)(3 - (-2))
= 10/3.

I hope this helps!