Answer:
x = 0
y = 2
z = 2
Step-by-step explanation:
-5x + 5y - 5z = 0
-5x = -5y + 5z
x = y - z
10x + 2y - 5z = -6
10(y - z) + 2y - 5z = -6
10y - 10z + 2y - 5z = -6
12y - 15z = -6
12y = 15z - 6
y = [tex]\frac{5}{4} z - \frac{1}{2}[/tex]
-5x + 2y + 3z = 10
-5(y - z) + 2(5/4z - 1/2) + 3z = 10
-5y + 5z + 5/2z - 1 + 3z = 10
-5y + 21/2z - 1 = 10
-5y + 21/2z = 11
21/2z = 11 + 5y
21z = 22 + 10y
z = [tex]\frac{22 + 10y}{21}[/tex]
_________
x = y - z
y = [tex]\frac{5}{4} z - \frac{1}{2}[/tex]
z = [tex]\frac{22 + 10y}{21}[/tex]
y = [tex]\frac{5}{4} (\frac{22 + 10y}{21} ) - \frac{1}{2}[/tex] = [tex]\frac{110 + 50y}{84} - \frac{1}{2}[/tex] = [tex]\frac{110 + 50y - 42}{84}[/tex] = [tex]\frac{68 + 50y}{84}[/tex] = [tex]\frac{17}{21} + \frac{25}{42} y[/tex]
y - [tex]\frac{25}{42} y[/tex] = [tex]\frac{17}{21}[/tex]
[tex]\frac{42}{42} y - \frac{25}{42} y = \frac{17}{21}[/tex]
[tex]\frac{17}{42} y = \frac{17}{21}[/tex]
17y = [tex]\frac{714}{21}[/tex]
17y = 34
y = 2
z = [tex]\frac{22 + 10y}{21}[/tex] = [tex]\frac{22 + 10(2)}{21} = \frac{42}{21}[/tex]
z = 2
x = y - z = 2 - 2
x = 0
