I am so rusty...solve for both X and Y?

You can certainly solve for x and y, but without another equation you can't find the 'value' of x or y. When they say solve for a variable they mean have it alone on one side of the = sign and all the other stuff on the other.

7x + 8y = 81. We'll solve for x first.

7x = 81 - 8y

x = (81 - 8y) / 7 This is the answer solved for x.

7x + 8y = 81. We'll solve for y now.

8y = 81 - 7x

y = (81 - 7x) / 8 This is the answer solved for y.

for x let y be 0. 7x+8(0)=81, 7x=81, 7x/7+81/7, x=11.5 or 81/7. for y let x=0. 7(0)+8y=81, 8y=81

8y/8=81/8. y=81/8 or y=10.1

y= (81-7x)/8

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Now plug this y value into the original

7x + 8(81-7x/8) = 81

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Solve for x

Then plug this x value into the original to get the y value.

you can't solve for x and y unless there is a second equation