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7x=y-1
Subtract 1 from both sides.
\frac{7x}{7}=\frac{y-1}{7}
Divide both sides by 7.
x=\frac{y-1}{7}
Dividing by 7 undoes the multiplication by 7.
y=7x+1
Swap sides so that all variable terms are on the left hand side.