Solve for y, x, z
x=4
y=11
z=11
Share
Copied to clipboard
2x+3=z
Substitute 2x+3 for y in the equation y=z.
x=-\frac{3}{2}+\frac{1}{2}z
Solve 2x+3=z for x.
z=5\left(-\frac{3}{2}+\frac{1}{2}z\right)-9
Substitute -\frac{3}{2}+\frac{1}{2}z for x in the equation z=5x-9.
z=11
Solve z=5\left(-\frac{3}{2}+\frac{1}{2}z\right)-9 for z.
x=-\frac{3}{2}+\frac{1}{2}\times 11
Substitute 11 for z in the equation x=-\frac{3}{2}+\frac{1}{2}z.
x=4
Calculate x from x=-\frac{3}{2}+\frac{1}{2}\times 11.
y=2\times 4+3
Substitute 4 for x in the equation y=2x+3.
y=11
Calculate y from y=2\times 4+3.
y=11 x=4 z=11
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}