Solve for a
a=\frac{2b}{3}
Solve for b
b=\frac{3a}{2}
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3a+3b=6a+b
Combine 5a and -2a to get 3a.
3a+3b-6a=b
Subtract 6a from both sides.
-3a+3b=b
Combine 3a and -6a to get -3a.
-3a=b-3b
Subtract 3b from both sides.
-3a=-2b
Combine b and -3b to get -2b.
\frac{-3a}{-3}=-\frac{2b}{-3}
Divide both sides by -3.
a=-\frac{2b}{-3}
Dividing by -3 undoes the multiplication by -3.
a=\frac{2b}{3}
Divide -2b by -3.
3a+3b=6a+b
Combine 5a and -2a to get 3a.
3a+3b-b=6a
Subtract b from both sides.
3a+2b=6a
Combine 3b and -b to get 2b.
2b=6a-3a
Subtract 3a from both sides.
2b=3a
Combine 6a and -3a to get 3a.
\frac{2b}{2}=\frac{3a}{2}
Divide both sides by 2.
b=\frac{3a}{2}
Dividing by 2 undoes the multiplication by 2.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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}