Solve for x
x=\frac{-3y-7}{4}
Solve for y
y=\frac{-4x-7}{3}
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-2\left(2x-1\right)=3\left(y+3\right)
Multiply both sides of the equation by 6, the least common multiple of -3,2.
-4x+2=3\left(y+3\right)
Use the distributive property to multiply -2 by 2x-1.
-4x+2=3y+9
Use the distributive property to multiply 3 by y+3.
-4x=3y+9-2
Subtract 2 from both sides.
-4x=3y+7
Subtract 2 from 9 to get 7.
\frac{-4x}{-4}=\frac{3y+7}{-4}
Divide both sides by -4.
x=\frac{3y+7}{-4}
Dividing by -4 undoes the multiplication by -4.
x=\frac{-3y-7}{4}
Divide 3y+7 by -4.
-2\left(2x-1\right)=3\left(y+3\right)
Multiply both sides of the equation by 6, the least common multiple of -3,2.
-4x+2=3\left(y+3\right)
Use the distributive property to multiply -2 by 2x-1.
-4x+2=3y+9
Use the distributive property to multiply 3 by y+3.
3y+9=-4x+2
Swap sides so that all variable terms are on the left hand side.
3y=-4x+2-9
Subtract 9 from both sides.
3y=-4x-7
Subtract 9 from 2 to get -7.
\frac{3y}{3}=\frac{-4x-7}{3}
Divide both sides by 3.
y=\frac{-4x-7}{3}
Dividing by 3 undoes the multiplication by 3.
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}