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When solving for two equations with two variables, take one equation (it doesn't matter which one) and solve for one of the variables (it doesn't matter which one).
4x + 7y = 47
7y = 47 - 4x
y = 47/7 - (4/7)x
Now plug that value for the variable you solved for into the other equation
5x - 4y = -5
5x - 4(47/7 - (4/7)x) = -5
5x -188/7 + (16/7)x = -5
(51/7)x = 153/7
51x = 153
x = 3
Now plug that value into either equation to solve for the other variable.
4x + 7y = 47
4(3) + 7y = 47
12 + 7y = 47
7y = 35
y = 5
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