Question

Zuca comprou 2 canetas, 3 borrachas e um caderno por R$ 13,00. Zica comprou uma caneta e dois cadernos pagando R$ 14,00 e Zoca comprou duas borrachas e 4 canetas por R$ 10,00. Utilizando o processo de determinantes, encontre quanto Zeca pagaria se comprasse um item de cada​

Answer 1

Resposta:

O Zeca gastaria R$ 9,00 comprando um item de cada.

Explicação passo-a-passo:

sendo:

x= caneta, y= borracha e z= caderno

Zuca: 2x+3y+z=13

Zica:  x+0y+2z=14

Zoca: 4x+2y+0z =10

$\left[\begin{array}{ccc}2&3&1\\1&0&2\\4&2&0\end{array}\right] .\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}13\\14\\10\end{array}\right]$

Resolvendo por Cramer:

$\Delta=\displaystyle \left[\begin{array}{ccc}2&3&1\\1&0&2\\4&2&0\end{array}\right] =(2).(0).(0)+(3).(2).(4)+(1).(2).(1)-(4).(0).(1)-(1).(3).(0)-(2).(2).(2)=26+(-8)=18$

$\Delta x=\displaystyle \left[\begin{array}{ccc}13&3&1\\14&0&2\\10&2&0\end{array}\right] =(13).(0).(0)+(3).(2).(10)+(14).(2).(1)-(10).(0).(1)-(14).(3).(0)-(2).(2).(13)=88+(-52)=36$

$\Delta y=\displaystyle \left[\begin{array}{ccc}2&13&1\\1&14&2\\4&10&0\end{array}\right] =(2).(14).(0)+(13).(2).(4)+(1).(10).(1)-(4).(14).(1)-(1).(13).(0)-(10).(2).(2)=114+(-96)=18$

$\Delta z=\displaystyle \left[\begin{array}{ccc}2&3&13\\1&0&14\\4&2&10\end{array}\right] =(2).(0).(10)+(3).(14).(4)+(1).(2).(13)-(4).(0).(13)-(1).(3).(10)-(2).(14).(2)=194+(-86)=108$

$\displaystyle x=\frac{\Delta x}{\Delta} =\frac{36}{18} =2\\\\\\y=\frac{\Delta y}{\Delta} =\frac{18}{18} =1\\\\\\z=\frac{\Delta z}{\Delta} =\frac{108}{18} =6$

Zeca: x+y+z=2+1+6=9