Carilah penyelesaian dari s
aturan Cranner.
F.

Ask by Ruiz Maxwell. in Indonesia

Jan 16,2025

Question

Carilah penyelesaian dari s aturan Cranner. F. $$ \left[\begin{array}{l}x+3 y+2 z=13 \ 2 x+y+3 z=13 \ 3 x+2 y+z=10\end{array}ight] $$

UpStudy AI · Accepted Answer

Solve the system of equations $$ x+3y+2z=13;2x+y+3z=13;3x+2y+z=10 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}x+3y+2z=13\2x+y+3z=13\3x+2y+z=10\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=13-3y-2z\2x+y+3z=13\3x+2y+z=10\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$\left\{ \begin{array}{l}2\left(13-3y-2zight)+y+3z=13\3\left(13-3y-2zight)+2y+z=10\end{array}ight.$$
- step3: Simplify:
  $$\left\{ \begin{array}{l}26-5y-z=13\39-7y-5z=10\end{array}ight.$$
- step4: Solve the equation:
  $$\left\{ \begin{array}{l}z=13-5y\39-7y-5z=10\end{array}ight.$$
- step5: Substitute the value of $$z:$$
  $$39-7y-5\left(13-5yight)=10$$
- step6: Simplify:
  $$-26+18y=10$$
- step7: Move the constant to the right side:
  $$18y=10+26$$
- step8: Add the numbers:
  $$18y=36$$
- step9: Divide both sides:
  $$\frac{18y}{18}=\frac{36}{18}$$
- step10: Divide the numbers:
  $$y=2$$
- step11: Substitute the value of $$y:$$
  $$z=13-5	imes 2$$
- step12: Simplify:
  $$z=3$$
- step13: Substitute the values of $$y,z:$$
  $$x=13-3	imes 2-2	imes 3$$
- step14: Simplify:
  $$x=1$$
- step15: Calculate:
  $$\left\{ \begin{array}{l}x=1\y=2\z=3\end{array}ight.$$
- step16: Check the solution:
  $$\left\{ \begin{array}{l}x=1\y=2\z=3\end{array}ight.$$
- step17: Rewrite:
  $$\left(x,y,zight) = \left(1,2,3ight)$$
Penyelesaian dari sistem persamaan linear yang diberikan adalah $$ (x, y, z) = (1, 2, 3) $$.
The solution to the system of equations is $$ x = 1 $$, $$ y = 2 $$, and $$ z = 3 $$.

Carilah penyelesaian dari s
aturan Cranner.
F.

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