Solve for x
x=-\frac{15y}{2}
Solve for y
y=-\frac{2x}{15}
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2x+5\times 3y=0
Multiply both sides of the equation by 10, the least common multiple of 5,2.
2x+15y=0
Multiply 5 and 3 to get 15.
2x=-15y
Subtract 15y from both sides. Anything subtracted from zero gives its negation.
\frac{2x}{2}=-\frac{15y}{2}
Divide both sides by 2.
x=-\frac{15y}{2}
Dividing by 2 undoes the multiplication by 2.
2x+5\times 3y=0
Multiply both sides of the equation by 10, the least common multiple of 5,2.
2x+15y=0
Multiply 5 and 3 to get 15.
15y=-2x
Subtract 2x from both sides. Anything subtracted from zero gives its negation.
\frac{15y}{15}=-\frac{2x}{15}
Divide both sides by 15.
y=-\frac{2x}{15}
Dividing by 15 undoes the multiplication by 15.
Examples
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{ 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}