Solve for x
x=\frac{4y}{3}
Solve for y
y=\frac{3x}{4}
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2x+3y-5x=-y
Subtract 5x from both sides.
-3x+3y=-y
Combine 2x and -5x to get -3x.
-3x=-y-3y
Subtract 3y from both sides.
-3x=-4y
Combine -y and -3y to get -4y.
\frac{-3x}{-3}=-\frac{4y}{-3}
Divide both sides by -3.
x=-\frac{4y}{-3}
Dividing by -3 undoes the multiplication by -3.
x=\frac{4y}{3}
Divide -4y by -3.
2x+3y+y=5x
Add y to both sides.
2x+4y=5x
Combine 3y and y to get 4y.
4y=5x-2x
Subtract 2x from both sides.
4y=3x
Combine 5x and -2x to get 3x.
\frac{4y}{4}=\frac{3x}{4}
Divide both sides by 4.
y=\frac{3x}{4}
Dividing by 4 undoes the multiplication by 4.
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}