Solve for x
x=\frac{z}{4}+\frac{3y}{2z}
z\neq 0
Solve for y
y=-\frac{z\left(z-4x\right)}{6}
z\neq 0
Quiz
Linear Equation
5 problems similar to:
\frac { 2 x } { 3 } = \frac { y } { z } + \frac { z } { 6 }
Share
Copied to clipboard
2z\times 2x=6y+zz
Multiply both sides of the equation by 6z, the least common multiple of 3,z,6.
2z\times 2x=6y+z^{2}
Multiply z and z to get z^{2}.
4zx=6y+z^{2}
Multiply 2 and 2 to get 4.
\frac{4zx}{4z}=\frac{6y+z^{2}}{4z}
Divide both sides by 4z.
x=\frac{6y+z^{2}}{4z}
Dividing by 4z undoes the multiplication by 4z.
x=\frac{z}{4}+\frac{3y}{2z}
Divide 6y+z^{2} by 4z.
2z\times 2x=6y+zz
Multiply both sides of the equation by 6z, the least common multiple of 3,z,6.
2z\times 2x=6y+z^{2}
Multiply z and z to get z^{2}.
4zx=6y+z^{2}
Multiply 2 and 2 to get 4.
6y+z^{2}=4zx
Swap sides so that all variable terms are on the left hand side.
6y=4zx-z^{2}
Subtract z^{2} from both sides.
6y=4xz-z^{2}
The equation is in standard form.
\frac{6y}{6}=\frac{z\left(4x-z\right)}{6}
Divide both sides by 6.
y=\frac{z\left(4x-z\right)}{6}
Dividing by 6 undoes the multiplication 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}