Solve for x
x=\frac{y}{2}
Solve for y
y=2x
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2x+y\times 5-12x=0
Subtract 12x from both sides.
-10x+y\times 5=0
Combine 2x and -12x to get -10x.
-10x=-y\times 5
Subtract y\times 5 from both sides. Anything subtracted from zero gives its negation.
-10x=-5y
Multiply -1 and 5 to get -5.
\frac{-10x}{-10}=-\frac{5y}{-10}
Divide both sides by -10.
x=-\frac{5y}{-10}
Dividing by -10 undoes the multiplication by -10.
x=\frac{y}{2}
Divide -5y by -10.
y\times 5=12x-2x
Subtract 2x from both sides.
y\times 5=10x
Combine 12x and -2x to get 10x.
5y=10x
The equation is in standard form.
\frac{5y}{5}=\frac{10x}{5}
Divide both sides by 5.
y=\frac{10x}{5}
Dividing by 5 undoes the multiplication by 5.
y=2x
Divide 10x by 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}