book Maths Puzzle Numerical Ability

The problem asks me to solve usling any method.
5x+6y=14
y=4x-17
I am not sure which method to use. I tried both but did not come out with the same answer both times! Thanks for your help!

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book Other Question

the gym is 21 years newer than the auditorium. the gym is also 1/4 as old as the auditorium. how old is each building? Determine whether the following equations have a solution or not? Justify your answer.

a) 5x2 + 8x + 7 = 0
b) (7)1/2y2 - 6y - 13(7)1/2 = 0
c) 2x2 + x - 1 = 0
d) 4/3