Solve for x
x=\frac{6y-2}{5}
Solve for y
y=\frac{5x}{6}+\frac{1}{3}
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9x-\left(4x+1\right)=3\left(2y-1\right)
Multiply both sides of the equation by 9, the least common multiple of 9,3.
9x-4x-1=3\left(2y-1\right)
To find the opposite of 4x+1, find the opposite of each term.
5x-1=3\left(2y-1\right)
Combine 9x and -4x to get 5x.
5x-1=6y-3
Use the distributive property to multiply 3 by 2y-1.
5x=6y-3+1
Add 1 to both sides.
5x=6y-2
Add -3 and 1 to get -2.
\frac{5x}{5}=\frac{6y-2}{5}
Divide both sides by 5.
x=\frac{6y-2}{5}
Dividing by 5 undoes the multiplication by 5.
9x-\left(4x+1\right)=3\left(2y-1\right)
Multiply both sides of the equation by 9, the least common multiple of 9,3.
9x-4x-1=3\left(2y-1\right)
To find the opposite of 4x+1, find the opposite of each term.
5x-1=3\left(2y-1\right)
Combine 9x and -4x to get 5x.
5x-1=6y-3
Use the distributive property to multiply 3 by 2y-1.
6y-3=5x-1
Swap sides so that all variable terms are on the left hand side.
6y=5x-1+3
Add 3 to both sides.
6y=5x+2
Add -1 and 3 to get 2.
\frac{6y}{6}=\frac{5x+2}{6}
Divide both sides by 6.
y=\frac{5x+2}{6}
Dividing by 6 undoes the multiplication by 6.
y=\frac{5x}{6}+\frac{1}{3}
Divide 5x+2 by 6.
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}