Solve {l}{v-w+1=0}{-2u+4v+5=0}{u+2v+3w+7=0}

$$\left. \begin{array} { l } { v - w + 1 = 0 } \\ { - 2 u + 4 v + 5 = 0 } \\ { u + 2 v + 3 w + 7 = 0 } \end{array} \right.$$

Solve for v, w, u

$$v = -\frac{25}{14} = -1\frac{11}{14} \approx -1.785714286$$

$$w=-\frac{11}{14}\approx -0.785714286$$

$$u = -\frac{15}{14} = -1\frac{1}{14} \approx -1.071428571$$

Short Steps Using Substitution

Solve v-w+1=0 for v.

$$v=w-1$$

Substitute w-1 for v in the second and third equation.

$$-2u+4\left(w-1\right)+5=0 u+2\left(w-1\right)+3w+7=0$$

Solve these equations for w and u respectively.

$$w=-\frac{1}{4}+\frac{1}{2}u u=-5-5w$$

Substitute -\frac{1}{4}+\frac{1}{2}u for w in the equation u=-5-5w.

$$u=-5-5\left(-\frac{1}{4}+\frac{1}{2}u\right)$$

Solve u=-5-5\left(-\frac{1}{4}+\frac{1}{2}u\right) for u.

$$u=-\frac{15}{14}$$

Substitute -\frac{15}{14} for u in the equation w=-\frac{1}{4}+\frac{1}{2}u.

$$w=-\frac{1}{4}+\frac{1}{2}\left(-\frac{15}{14}\right)$$

Calculate w from w=-\frac{1}{4}+\frac{1}{2}\left(-\frac{15}{14}\right).

$$w=-\frac{11}{14}$$

Substitute -\frac{11}{14} for w in the equation v=w-1.

$$v=-\frac{11}{14}-1$$

Calculate v from v=-\frac{11}{14}-1.

$$v=-\frac{25}{14}$$

The system is now solved.

$$v=-\frac{25}{14} w=-\frac{11}{14} u=-\frac{15}{14}$$