\left\{ \begin{array} { l } { 9 a + 3 b + c = 0 } \\ { c = 3 } \\ { a - b + c = 0 } \end{array} \right.
Solve for a, b, c
a=-1
b=2
c=3
Share
Copied to clipboard
c=3 9a+3b+c=0 a-b+c=0
Reorder the equations.
9a+3b+3=0 a-b+3=0
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=-1-3a-3
Substitute -1-3a for b in the equation a=b-3.
a=-1
Solve a=-1-3a-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}