solve by elimination

Question

-4x - 5y - z = 18

-2x - 5y + 5z = 12

-2x + 5y + 2z = 4

Answer 1

eliminates y......

changes ALL of the signs:

4x + 5y + z = -18

2x + 5y - 5z = -12

2x - 5y - 2z = -4

Equation 1 - Equation 2:

2x + 6z = -6

Equation 2 + equation 3:

4x - 7z = -16

2 by 2 system:

2x + 6z = -6

4x - 7z = -16

equation 2 - 2 * equation 1:

-19z = -16 - 2 * -6

= -16 - -12

= -4

z = 4/19

2x + 6(4/19) = -6

2x + 24/19 = -6

2x + 24/19 = -114/19

38x + 24 = -114

38x = -138

x = -138/38 = -69/19

-2x + 5y + 2z = 4

(-2)(-69/19) + 5y + 2(4/19) = 4

138/19 + 5y + 8/19 = 4

138 + 95y + 8 = 76

95y + 146 = 76

95y = -70

y = -70/95 = -14/19

(x = -69/19, y= -14/19, z = 4/19)

checks equation #1:

-4x - 5y - z = (-4)(-69/19) - 5(-14/19) - 4/19

= 276/19 + 70/19 - 4/19

= 342/19

= 18

so equation #1 checks!

checks equation #2:

-2x - 5y + 5z = (-2)(-69/19) - 5(-14/19) + 5 (4/19)

= 138/19 + 70/19 + 20/19

= 228/19

= 12

so equation #2 checks !!

checks equation #3:

-2x + 5y + 2z = (-2)(-69/19) + 5(-14/19) + 2(4/19)

= 138/19 - 70/19 + 8/19

= 76/19

= 4

so equation #3 checks !!!

The OFFICIAL ANswer is:

(x = -69/19, y= -14/19, z = 4/19)