Solve for a
a=\frac{x+5b}{10}
Solve for b
b=-\frac{x}{5}+2a
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x=10a-5b
Multiply both sides of the equation by 5.
10a-5b=x
Swap sides so that all variable terms are on the left hand side.
10a=x+5b
Add 5b to both sides.
\frac{10a}{10}=\frac{x+5b}{10}
Divide both sides by 10.
a=\frac{x+5b}{10}
Dividing by 10 undoes the multiplication by 10.
a=\frac{b}{2}+\frac{x}{10}
Divide x+5b by 10.
x=10a-5b
Multiply both sides of the equation by 5.
10a-5b=x
Swap sides so that all variable terms are on the left hand side.
-5b=x-10a
Subtract 10a from both sides.
\frac{-5b}{-5}=\frac{x-10a}{-5}
Divide both sides by -5.
b=\frac{x-10a}{-5}
Dividing by -5 undoes the multiplication by -5.
b=-\frac{x}{5}+2a
Divide x-10a by -5.
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}