Solve for x
x=-\frac{5-y}{2\left(3-y\right)}
y\neq 3
Solve for y
y=\frac{6x+5}{2x+1}
x\neq -\frac{1}{2}
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y\left(2x+1\right)=2+\left(2x+1\right)\times 3
Variable x cannot be equal to -\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 2x+1.
2yx+y=2+\left(2x+1\right)\times 3
Use the distributive property to multiply y by 2x+1.
2yx+y=2+6x+3
Use the distributive property to multiply 2x+1 by 3.
2yx+y=5+6x
Add 2 and 3 to get 5.
2yx+y-6x=5
Subtract 6x from both sides.
2yx-6x=5-y
Subtract y from both sides.
\left(2y-6\right)x=5-y
Combine all terms containing x.
\frac{\left(2y-6\right)x}{2y-6}=\frac{5-y}{2y-6}
Divide both sides by 2y-6.
x=\frac{5-y}{2y-6}
Dividing by 2y-6 undoes the multiplication by 2y-6.
x=\frac{5-y}{2\left(y-3\right)}
Divide -y+5 by 2y-6.
x=\frac{5-y}{2\left(y-3\right)}\text{, }x\neq -\frac{1}{2}
Variable x cannot be equal to -\frac{1}{2}.
Examples
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y = 3x + 4
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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
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