How do you solve using gaussian elimination or gauss-jordan elimination, y+z=-3, x-y+z=-7, x+y=2?

Mar 28, 2017

$x = 0 , y = 2 \mathmr{and} z = - 5$

Explanation:

${r}_{1} \to$ $0$........$1$........$1$........$- 3$
${r}_{2} \to$ $1$....$- 1$........$1$........$- 7$
${r}_{3} \to$ $1$........$1$........$0$............$2$

${r}_{1} = {r}_{1} + {r}_{2}$
$1$........$0$........$2$........$- 10$
$1$....$- 1$........$1$........$- 7$
$1$........$1$........$0$............$2$

${r}_{2} = {r}_{1} - {r}_{2}$
$1$........$0$........$2$........$- 10$
$0$........$1$........$1$........$- 3$
$1$........$1$........$0$............$2$

${r}_{3} = {r}_{3} - {r}_{1}$
$1$........$0$........$2$........$- 10$
$0$........$1$........$1$........$- 3$
$0$........$1$....$- 2$...........$12$

${r}_{3} = {r}_{3} - {r}_{2}$
$1$........$0$........$2$........$- 10$
$0$........$1$........$1$........$- 3$
$0$........$0$....$- 3$...........$15$

${r}_{3} = {r}_{3} / - 3$
$1$........$0$........$2$........$- 10$
$0$........$1$........$1$........$- 3$
$0$........$0$........$1$........$- 5$

${r}_{2} = {r}_{2} - {r}_{3}$
$1$........$0$........$2$........$- 10$
$0$........$1$........$0$............$2$
$0$........$0$........$1$........$- 5$

${r}_{1} = {r}_{1} - 2 {r}_{3}$
$1$........$0$........$0$...........$0$
$0$........$1$........$0$............$2$
$0$........$0$........$1$........$- 5$