Solve for x, y (complex solution)
\left\{\begin{matrix}\\x=0\text{, }y=0\text{, }&\text{unconditionally}\\x=\frac{3y}{2-P}\text{, }y\in \mathrm{C}\text{, }&P\neq 2\text{ and }Q=4\\x\in \mathrm{C}\text{, }y=0\text{, }&P=2\text{ and }Q=4\end{matrix}\right.
Solve for x, y
\left\{\begin{matrix}\\x=0\text{, }y=0\text{, }&\text{unconditionally}\\x=\frac{3y}{2-P}\text{, }y\in \mathrm{R}\text{, }&P\neq 2\text{ and }Q=4\\x\in \mathrm{R}\text{, }y=0\text{, }&P=2\text{ and }Q=4\end{matrix}\right.
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Qx-4x=0
Consider the second equation. Subtract 4x from both sides.
\left(Q-4\right)x=0
Combine all terms containing x,y.
Px-2x=-3y
Consider the first equation. Subtract 2x from both sides.
Px-2x+3y=0
Add 3y to both sides.
\left(P-2\right)x+3y=0
Combine all terms containing x,y.
\left(Q-4\right)x=0,\left(P-2\right)x+3y=0
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
\left(Q-4\right)x=0
Pick one of the two equations which is more simple to solve for x by isolating x on the left hand side of the equal sign.
x=0
Divide both sides by -4+Q.
3y=0
Substitute 0 for x in the other equation, \left(P-2\right)x+3y=0.
y=0
Divide both sides by 3.
x=0,y=0
The system is now solved.
Qx-4x=0
Consider the second equation. Subtract 4x from both sides.
\left(Q-4\right)x=0
Combine all terms containing x,y.
Px-2x=-3y
Consider the first equation. Subtract 2x from both sides.
Px-2x+3y=0
Add 3y to both sides.
\left(P-2\right)x+3y=0
Combine all terms containing x,y.
\left(Q-4\right)x=0,\left(P-2\right)x+3y=0
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
\left(Q-4\right)x=0
Pick one of the two equations which is more simple to solve for x by isolating x on the left hand side of the equal sign.
x=0
Divide both sides by -4+Q.
3y=0
Substitute 0 for x in the other equation, \left(P-2\right)x+3y=0.
y=0
Divide both sides by 3.
x=0,y=0
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
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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}