Solve for x
x=\frac{3y}{4}-\frac{z}{2}
Solve for y
y=\frac{2\left(2x+z\right)}{3}
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8x+4z=6y
Add 6y to both sides. Anything plus zero gives itself.
8x=6y-4z
Subtract 4z from both sides.
\frac{8x}{8}=\frac{6y-4z}{8}
Divide both sides by 8.
x=\frac{6y-4z}{8}
Dividing by 8 undoes the multiplication by 8.
x=\frac{3y}{4}-\frac{z}{2}
Divide 6y-4z by 8.
-6y+4z=-8x
Subtract 8x from both sides. Anything subtracted from zero gives its negation.
-6y=-8x-4z
Subtract 4z from both sides.
\frac{-6y}{-6}=\frac{-8x-4z}{-6}
Divide both sides by -6.
y=\frac{-8x-4z}{-6}
Dividing by -6 undoes the multiplication by -6.
y=\frac{4x+2z}{3}
Divide -8x-4z by -6.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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}