Solve for x
\left\{\begin{matrix}x=\frac{y-2z-10}{z+2}\text{, }&z\neq -2\\x\in \mathrm{R}\text{, }&y=6\text{ and }z=-2\end{matrix}\right.
Solve for y
y=xz+2x+2z+10
Share
Copied to clipboard
x^{2}+y=x^{2}+xz+2x+2z+10
Use the distributive property to multiply x+2 by x+z.
x^{2}+y-x^{2}=xz+2x+2z+10
Subtract x^{2} from both sides.
y=xz+2x+2z+10
Combine x^{2} and -x^{2} to get 0.
xz+2x+2z+10=y
Swap sides so that all variable terms are on the left hand side.
xz+2x+10=y-2z
Subtract 2z from both sides.
xz+2x=y-2z-10
Subtract 10 from both sides.
\left(z+2\right)x=y-2z-10
Combine all terms containing x.
\frac{\left(z+2\right)x}{z+2}=\frac{y-2z-10}{z+2}
Divide both sides by 2+z.
x=\frac{y-2z-10}{z+2}
Dividing by 2+z undoes the multiplication by 2+z.
x^{2}+y=x^{2}+xz+2x+2z+10
Use the distributive property to multiply x+2 by x+z.
y=x^{2}+xz+2x+2z+10-x^{2}
Subtract x^{2} from both sides.
y=xz+2x+2z+10
Combine x^{2} and -x^{2} to get 0.
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}