Solve for x
x=\frac{5y}{7}
Solve for y
y=\frac{7x}{5}
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2\left(4x-y\right)=x+3y
Multiply both sides of the equation by 4, the least common multiple of 2,4.
8x-2y=x+3y
Use the distributive property to multiply 2 by 4x-y.
8x-2y-x=3y
Subtract x from both sides.
7x-2y=3y
Combine 8x and -x to get 7x.
7x=3y+2y
Add 2y to both sides.
7x=5y
Combine 3y and 2y to get 5y.
\frac{7x}{7}=\frac{5y}{7}
Divide both sides by 7.
x=\frac{5y}{7}
Dividing by 7 undoes the multiplication by 7.
2\left(4x-y\right)=x+3y
Multiply both sides of the equation by 4, the least common multiple of 2,4.
8x-2y=x+3y
Use the distributive property to multiply 2 by 4x-y.
8x-2y-3y=x
Subtract 3y from both sides.
8x-5y=x
Combine -2y and -3y to get -5y.
-5y=x-8x
Subtract 8x from both sides.
-5y=-7x
Combine x and -8x to get -7x.
\frac{-5y}{-5}=-\frac{7x}{-5}
Divide both sides by -5.
y=-\frac{7x}{-5}
Dividing by -5 undoes the multiplication by -5.
y=\frac{7x}{5}
Divide -7x 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}