\left\{ \begin{array} { l } { 0 = 9 a - 3 b + c } \\ { 3 = c } \\ { 0 = a + b + c } \end{array} \right.
Solve for a, b, c
a=-1
b=-2
c=3
Share
Copied to clipboard
3=c 0=9a-3b+c 0=a+b+c
Reorder the equations.
c=3
Solve 3=c for c.
0=9a-3b+3 0=a+b+3
Substitute 3 for c in the second and third equation.
b=1+3a a=-b-3
Solve these equations for b and a respectively.
a=-\left(1+3a\right)-3
Substitute 1+3a for b in the equation a=-b-3.
a=-1
Solve a=-\left(1+3a\right)-3 for a.
b=1+3\left(-1\right)
Substitute -1 for a in the equation b=1+3a.
b=-2
Calculate b from b=1+3\left(-1\right).
a=-1 b=-2 c=3
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
\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}