in this case, substitution is your obvious choice
sub the 2nd into the 1st.
2(4y+1) - 3y = 12
8y + 2 - 3y = 12
5y = 10
y = 2
sub into the 2nd
x = 4(2) + 1 = 9
x = 9 , y = 2
2x-3y=12
x=4y+1
substitution, elemenation
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