Solve for x
x=-\frac{y}{14}
Solve for y
y=-14x
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3\left(2y+3x\right)=5\left(y-x\right)
Multiply both sides of the equation by 15, the least common multiple of 5,3.
6y+9x=5\left(y-x\right)
Use the distributive property to multiply 3 by 2y+3x.
6y+9x=5y-5x
Use the distributive property to multiply 5 by y-x.
6y+9x+5x=5y
Add 5x to both sides.
6y+14x=5y
Combine 9x and 5x to get 14x.
14x=5y-6y
Subtract 6y from both sides.
14x=-y
Combine 5y and -6y to get -y.
\frac{14x}{14}=-\frac{y}{14}
Divide both sides by 14.
x=-\frac{y}{14}
Dividing by 14 undoes the multiplication by 14.
3\left(2y+3x\right)=5\left(y-x\right)
Multiply both sides of the equation by 15, the least common multiple of 5,3.
6y+9x=5\left(y-x\right)
Use the distributive property to multiply 3 by 2y+3x.
6y+9x=5y-5x
Use the distributive property to multiply 5 by y-x.
6y+9x-5y=-5x
Subtract 5y from both sides.
y+9x=-5x
Combine 6y and -5y to get y.
y=-5x-9x
Subtract 9x from both sides.
y=-14x
Combine -5x and -9x to get -14x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}