Solve for x
x=-\frac{4y}{5}
Solve for y
y=-\frac{5x}{4}
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6x+y-x=-3y
Subtract x from both sides.
5x+y=-3y
Combine 6x and -x to get 5x.
5x=-3y-y
Subtract y from both sides.
5x=-4y
Combine -3y and -y to get -4y.
\frac{5x}{5}=-\frac{4y}{5}
Divide both sides by 5.
x=-\frac{4y}{5}
Dividing by 5 undoes the multiplication by 5.
6x+y+3y=x
Add 3y to both sides.
6x+4y=x
Combine y and 3y to get 4y.
4y=x-6x
Subtract 6x from both sides.
4y=-5x
Combine x and -6x to get -5x.
\frac{4y}{4}=-\frac{5x}{4}
Divide both sides by 4.
y=-\frac{5x}{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}