Question

Solve the system algebraically. PLEASE

Answer 1

x = 0

y = 2

z = 2

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 =
`(5)/(4) z - (1)/(2)`

-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 =
`(22 + 10y)/(21)`

_________

x = y - z

y =
`(5)/(4) z - (1)/(2)`

z =
`(22 + 10y)/(21)`

y =
`(5)/(4) ((22 + 10y)/(21) ) - (1)/(2)` =
`(110 + 50y)/(84) - (1)/(2)` =
`(110 + 50y - 42)/(84)` =
`(68 + 50y)/(84)` =
`(17)/(21) + (25)/(42) y`

y -
`(25)/(42) y` =
`(17)/(21)`

`(42)/(42) y - (25)/(42) y = (17)/(21)`

`(17)/(42) y = (17)/(21)`

17y =
`(714)/(21)`

17y = 34

y = 2

z =
`(22 + 10y)/(21)` =
`(22 + 10(2))/(21) = (42)/(21)`

z = 2

x = y - z = 2 - 2

x = 0