Solve for x
x=\frac{5y}{4}-z
Solve for y
y=\frac{4\left(x+z\right)}{5}
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4x+4z=5y
Swap sides so that all variable terms are on the left hand side.
4x=5y-4z
Subtract 4z from both sides.
\frac{4x}{4}=\frac{5y-4z}{4}
Divide both sides by 4.
x=\frac{5y-4z}{4}
Dividing by 4 undoes the multiplication by 4.
x=\frac{5y}{4}-z
Divide 5y-4z by 4.
5y=4x+4z
The equation is in standard form.
\frac{5y}{5}=\frac{4x+4z}{5}
Divide both sides by 5.
y=\frac{4x+4z}{5}
Dividing by 5 undoes the multiplication by 5.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}