They are never perpendicular. They will be parallel and will never meet!
2a+1b=27.50
4a+2b=59.50
Multiply first equation by -4 and the second by 2 so you can drop off the a values then add the equations together. Then solve for b. You should get b=6.
Then plug b into one of the original equations and solve for a and you should get 10.75
So a plate of spaghetti is $10.75 and a salad is $6.
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That would be 16.625 pounds and/or 266 pounds