Solve for x
x=\frac{2y}{5}
Solve for y
y=\frac{5x}{2}
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5x+3x+2y=5x-2x+4y
Combine 3x and 2x to get 5x.
8x+2y=5x-2x+4y
Combine 5x and 3x to get 8x.
8x+2y=3x+4y
Combine 5x and -2x to get 3x.
8x+2y-3x=4y
Subtract 3x from both sides.
5x+2y=4y
Combine 8x and -3x to get 5x.
5x=4y-2y
Subtract 2y from both sides.
5x=2y
Combine 4y and -2y to get 2y.
\frac{5x}{5}=\frac{2y}{5}
Divide both sides by 5.
x=\frac{2y}{5}
Dividing by 5 undoes the multiplication by 5.
5x+3x+2y=5x-2x+4y
Combine 3x and 2x to get 5x.
8x+2y=5x-2x+4y
Combine 5x and 3x to get 8x.
8x+2y=3x+4y
Combine 5x and -2x to get 3x.
8x+2y-4y=3x
Subtract 4y from both sides.
8x-2y=3x
Combine 2y and -4y to get -2y.
-2y=3x-8x
Subtract 8x from both sides.
-2y=-5x
Combine 3x and -8x to get -5x.
\frac{-2y}{-2}=-\frac{5x}{-2}
Divide both sides by -2.
y=-\frac{5x}{-2}
Dividing by -2 undoes the multiplication by -2.
y=\frac{5x}{2}
Divide -5x by -2.
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}