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-10k=5x-4y
Swap sides so that all variable terms are on the left hand side.
\frac{-10k}{-10}=\frac{5x-4y}{-10}
Divide both sides by -10.
k=\frac{5x-4y}{-10}
Dividing by -10 undoes the multiplication by -10.
k=\frac{2y}{5}-\frac{x}{2}
Divide 5x-4y by -10.
5x=-10k+4y
Add 4y to both sides.
5x=4y-10k
The equation is in standard form.
\frac{5x}{5}=\frac{4y-10k}{5}
Divide both sides by 5.
x=\frac{4y-10k}{5}
Dividing by 5 undoes the multiplication by 5.
x=\frac{4y}{5}-2k
Divide -10k+4y by 5.