Solve for x
x=\frac{-5y-2}{3}
Solve for y
y=\frac{-3x-2}{5}
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y=\frac{-3x-2}{5}
Multiply both numerator and denominator by -1.
y=-\frac{3}{5}x-\frac{2}{5}
Divide each term of -3x-2 by 5 to get -\frac{3}{5}x-\frac{2}{5}.
-\frac{3}{5}x-\frac{2}{5}=y
Swap sides so that all variable terms are on the left hand side.
-\frac{3}{5}x=y+\frac{2}{5}
Add \frac{2}{5} to both sides.
\frac{-\frac{3}{5}x}{-\frac{3}{5}}=\frac{y+\frac{2}{5}}{-\frac{3}{5}}
Divide both sides of the equation by -\frac{3}{5}, which is the same as multiplying both sides by the reciprocal of the fraction.
x=\frac{y+\frac{2}{5}}{-\frac{3}{5}}
Dividing by -\frac{3}{5} undoes the multiplication by -\frac{3}{5}.
x=\frac{-5y-2}{3}
Divide y+\frac{2}{5} by -\frac{3}{5} by multiplying y+\frac{2}{5} by the reciprocal of -\frac{3}{5}.
y=\frac{-3x-2}{5}
Multiply both numerator and denominator by -1.
y=-\frac{3}{5}x-\frac{2}{5}
Divide each term of -3x-2 by 5 to get -\frac{3}{5}x-\frac{2}{5}.
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}