7x - 3y = 37
2x - y = 12
You can eliminate y by multiplying both sides of equation 2 by minus 3 and then add:
7x - 3y = 37
-6x + 3y = -36
x = 1
substitute x =1 into either equation and solve y
2(1) -y =12
-y = 10
y = -10
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If you multiply or divide an equation by any non-zero number, the two sides of the equation remain equal. This property is almost always needed for solving equations in which the variables have coefficients other than 1.
x-9y
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For a linear I can see no advantage in the table method.