Question

The system of equations 4x+y+2z=5,x-5y+3z=10,9x+7z=20 has​

Answer 1

Answer:

( - 0.5, 0, 3.5)

Step-by-step explanation:

4x + y + 2z = 5

x - 5y + 3z = 10

9x + 0y + 7z = 20

Δ = $\left[\begin{array}{ccc}4&1&2\\1&-5&3\\9&0&7\end{array}\right]$ = 4(-5)(7) + 1(3)(9) + 2(1)(0) - 1(1)(7) - 4(3)(0) - 2(-5)(9) = - 30

$A_{x} = \left[\begin{array}{ccc}5&1&2\\10&-5&3\\20&0&7\end{array}\right]$ = 15

$A_{y}=\left[\begin{array}{ccc}4&5&2\\1&10&3\\9&20&7\end{array}\right] = 0$

$A_{z} = \left[\begin{array}{ccc}4&1&5\\1&-5&10\\9&0&20\end{array}\right] = - 105$

x = $\frac{A_{x} }{A} = \frac{15}{-30} = - \frac{1}{2} = - 0.5$

$y = \frac{A_{y}}{A} = \frac{0}{-30} = 0$

$z=\frac{A_{z}}{A} = \frac{-105}{-30} = 3.5$

( - 0.5, 0, 3.5)