Solve for x, y, z
x=1
y=7
z=6
Share
Copied to clipboard
x=3y-3z-2
Solve -x+3y-3z=2 for x.
2\left(3y-3z-2\right)-y+2z=7
Substitute 3y-3z-2 for x in the equation 2x-y+2z=7.
y=z+1 z=\frac{5}{4}y-\frac{11}{4}
Solve the second equation for y and the third equation for z.
z=\frac{5}{4}\left(z+1\right)-\frac{11}{4}
Substitute z+1 for y in the equation z=\frac{5}{4}y-\frac{11}{4}.
z=6
Solve z=\frac{5}{4}\left(z+1\right)-\frac{11}{4} for z.
y=6+1
Substitute 6 for z in the equation y=z+1.
y=7
Calculate y from y=6+1.
x=3\times 7-3\times 6-2
Substitute 7 for y and 6 for z in the equation x=3y-3z-2.
x=1
Calculate x from x=3\times 7-3\times 6-2.
x=1 y=7 z=6
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}