Question

Por meio de escolamentor resolva os sistemas

A) 3x-y+z=2
X-2y-z=0
2x+y+2z=2

B) x+2y+z=13
2x+y+z=7,5
4x+3y+z=14,5

Answer 1

$b \: \: d = |1 \: 2 \: 1 \\ 2 \: 1 \: 1 \\ 4 \: 3 \: 1| \\ \\ d_{1} |13 \: 2 \: 1 \\ 7.5 \: 1 \: 1 \\ 14.5 \: 3 \: 1 \\ \\ d_{2} |1 \: 13 \: 1 \\ 2 \: 7.5 \: 1 \\ 4 \: 14.5 \: 1| \\ \\ d_{3} |1 \: 2 \: 13 \\ 2 \: 1 \: 7.5 \\ 4 \: 3 \: 14.5| \\ \\ d = 4 \\ d_{1} = - 4 \\ d_{2} = 18 \\ d_{3} = 20 \\ \\ x = - 1 \\ y = \frac{9}{2} \\ z = 5$

$a \: \: 3 x - y + z = 2 \\ x - 2y - z = 0 \\ 2x + y + 2z = 2 \\ \\ 3x - y + z = 2 \\ x = 2y + z \\ 2x + y + 2z = 2 \\ \\ 3(2y + z) - y + z = 2 \\ 2(2y + z) + y + 2z = 2 \\ \\ 5y + 4z = 2 \\ - 5y - 4z = - 2 \\ \\ 0 = 0 \\ \\ z = \frac{1}{2} - \frac{5}{4} y \\ \\ x = 2y + \frac{1}{2} - \frac{5}{4} y \\ x = \frac{3}{4} y + \frac{1}{2}$