Solve for x
x=3y-1
Solve for y
y=\frac{x+1}{3}
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-3\left(y-2\right)=-\left(x-5\right)
Multiply both sides of the equation by 6, the least common multiple of -2,-6.
-3y+6=-\left(x-5\right)
Use the distributive property to multiply -3 by y-2.
-3y+6=-x+5
To find the opposite of x-5, find the opposite of each term.
-x+5=-3y+6
Swap sides so that all variable terms are on the left hand side.
-x=-3y+6-5
Subtract 5 from both sides.
-x=-3y+1
Subtract 5 from 6 to get 1.
-x=1-3y
The equation is in standard form.
\frac{-x}{-1}=\frac{1-3y}{-1}
Divide both sides by -1.
x=\frac{1-3y}{-1}
Dividing by -1 undoes the multiplication by -1.
x=3y-1
Divide -3y+1 by -1.
-3\left(y-2\right)=-\left(x-5\right)
Multiply both sides of the equation by 6, the least common multiple of -2,-6.
-3y+6=-\left(x-5\right)
Use the distributive property to multiply -3 by y-2.
-3y+6=-x+5
To find the opposite of x-5, find the opposite of each term.
-3y=-x+5-6
Subtract 6 from both sides.
-3y=-x-1
Subtract 6 from 5 to get -1.
\frac{-3y}{-3}=\frac{-x-1}{-3}
Divide both sides by -3.
y=\frac{-x-1}{-3}
Dividing by -3 undoes the multiplication by -3.
y=\frac{x+1}{3}
Divide -x-1 by -3.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}