\left\{ \begin{array} { l } { \frac { 1 } { x + 3 } = \frac { 1 } { 4 } } \\ { \frac { 1 } { y + 5 } = \frac { 1 } { 6 } } \end{array} \right.
Solve for x, y
x=1
y=1
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4=x+3
Consider the first equation. Variable x cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by 4\left(x+3\right), the least common multiple of x+3,4.
x+3=4
Swap sides so that all variable terms are on the left hand side.
x=4-3
Subtract 3 from both sides.
x=1
Subtract 3 from 4 to get 1.
6=y+5
Consider the second equation. Variable y cannot be equal to -5 since division by zero is not defined. Multiply both sides of the equation by 6\left(y+5\right), the least common multiple of y+5,6.
y+5=6
Swap sides so that all variable terms are on the left hand side.
y=6-5
Subtract 5 from both sides.
y=1
Subtract 5 from 6 to get 1.
x=1 y=1
The system is now solved.
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}