\left\{ \begin{array} { l } { x + \gamma y = 1 } \\ { 2 + x = 2 } \end{array} \right.
Solve for x, y
x=0
y=\frac{1}{\gamma }
\gamma \neq 0
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x+2=2,x+\gamma y=1
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.
x+2=2
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
Subtract 2 from both sides of the equation.
\gamma y=1
Substitute 0 for x in the other equation, x+\gamma y=1.
y=\frac{1}{\gamma }
Divide both sides by \gamma .
x=0,y=\frac{1}{\gamma }
The system is now solved.
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
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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}