Solve for x
x=\frac{3y+1}{2}
Solve for y
y=\frac{2x-1}{3}
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2\left(x+7\right)=3\left(y+5\right)
Multiply both sides of the equation by 18, the least common multiple of 9,6.
2x+14=3\left(y+5\right)
Use the distributive property to multiply 2 by x+7.
2x+14=3y+15
Use the distributive property to multiply 3 by y+5.
2x=3y+15-14
Subtract 14 from both sides.
2x=3y+1
Subtract 14 from 15 to get 1.
\frac{2x}{2}=\frac{3y+1}{2}
Divide both sides by 2.
x=\frac{3y+1}{2}
Dividing by 2 undoes the multiplication by 2.
2\left(x+7\right)=3\left(y+5\right)
Multiply both sides of the equation by 18, the least common multiple of 9,6.
2x+14=3\left(y+5\right)
Use the distributive property to multiply 2 by x+7.
2x+14=3y+15
Use the distributive property to multiply 3 by y+5.
3y+15=2x+14
Swap sides so that all variable terms are on the left hand side.
3y=2x+14-15
Subtract 15 from both sides.
3y=2x-1
Subtract 15 from 14 to get -1.
\frac{3y}{3}=\frac{2x-1}{3}
Divide both sides by 3.
y=\frac{2x-1}{3}
Dividing by 3 undoes the multiplication by 3.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
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699 * 533
Matrix
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}