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System of equations with three equations and three variables

label Algebra
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I have to use elimination to figure out this problem, I can do it with 2 equations and 2 variables but I can't understand the 3

-3x + y - z = -10

-4x + 2y +3y = -1

2x + 3y -2z = = -5

Mar 20th, 2015

Multiply the first equation by -2 to get

6x - 2y + 2z = 20

Add the 3rd equation to that to get

8x + y = 15

Simplify the second equation to get

-4x + 5y = -1

Multiply that by -2 to get

-8x + 10y = -2

Add the 8x + y = 15 to that to get

11y = 13

y = 13/11

Plug that into 8x + y = 15

8x + 13/11 = 15

8x = 15 - 13/11 = 152/11

x = 19/11

Plug x and y into the first equation to get

-3(19/11) + 13/11 - z = -10

-57/11 + 13/11 - z = -10

-44/11 - z = -10

-4 - z = -10

z = -4 + 10

z = 6

Mar 20th, 2015

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