Solve for x
x=-\frac{3y-10}{3-y}
y\neq 3
Solve for y
y=-\frac{10-3x}{x-3}
x\neq 3
Graph
Share
Copied to clipboard
y\left(x-3\right)=2-x+\left(x-3\right)\times 4
Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3.
yx-3y=2-x+\left(x-3\right)\times 4
Use the distributive property to multiply y by x-3.
yx-3y=2-x+4x-12
Use the distributive property to multiply x-3 by 4.
yx-3y=2+3x-12
Combine -x and 4x to get 3x.
yx-3y=-10+3x
Subtract 12 from 2 to get -10.
yx-3y-3x=-10
Subtract 3x from both sides.
yx-3x=-10+3y
Add 3y to both sides.
\left(y-3\right)x=-10+3y
Combine all terms containing x.
\left(y-3\right)x=3y-10
The equation is in standard form.
\frac{\left(y-3\right)x}{y-3}=\frac{3y-10}{y-3}
Divide both sides by y-3.
x=\frac{3y-10}{y-3}
Dividing by y-3 undoes the multiplication by y-3.
x=\frac{3y-10}{y-3}\text{, }x\neq 3
Variable x cannot be equal to 3.
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}