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Let the operations Δ and □ be defined for all real numbers a and b as follows:

a Δ b=a-3b

a □ b=a+5b

If 8 Δ (3y)=(3y) □ 6, what is the value of y?

We are given a Δ b = a - 3b and a □ b = a + 5b.

It is given that a Δ b = a - 3b, so 8 Δ (3y) = 8 - 9y.

It is given that a □ b = a + 5b,, so (3y) □ 6 = 3y + 30.

If 8 - 9y = 3y + 30, add -3y-8 to both sides. This gives -12y = 22.

Dividing both sides by -12 gives y = -22/12.

The numerator and denominator can both be divided by 2, giving y = -11/6.

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