Question 126485


{{{x-y-2z=0}}}………………………………(1)

{{{-2x+5y+10z=-3}}}……………………….(2)

{{{3x+y=0}}}………………………………..(3)
	
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{{{x-y-2z=0}}}………………………………(1)…=>

{{{x = y + 2z}}}………………plug into (2)


{{{-2(y + 2z ) + 5y + 10z = -3}}} ……………………….(2)


{{{-2y - 4z  + 5y + 10z = -3}}}

{{{3y + 6z = -3}}}………………………(I)

Now plug {{{x}}} into (3)

{{{3(y + 2z )+y=0}}} ………………………………..(3)

{{{3y + 6z +y=0}}}

{{{4y + 6z =0}}}…………………………..(II)

subtract (II) from (I) to solve for  {{{y}}}


{{{3y + 6z = -3}}}………………………(I)
{{{4y + 6z =0}}}…………………………..(II)
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{{{3y-4y+6z-6z= -3 – 0}}}

{{{-y+cross(6z)-cross(6z) = -3 }}}

{{{highlight(y = 3) }}}

{{{3x+y=0}}} ………………………………..(3)…plug in {{{y}}} and find {{{x}}}

{{{3x+3=0}}}

{{{3x = -3}}}

{{{highlight(x = -1)}}}


{{{x-y-2z=0}}} ………………………………(1)….. plug in {{{x}}} and {{{y}}}, then find {{{z}}}

{{{-1-3-2z=0}}}

{{{-4-2z=0}}}

{{{-4 = 2z}}}

{{{-4/2 = z}}}

{{{highlight(z = -2) }}}


Check:


{{{x-y-2z=0}}} ………………………………(1)

{{{-1-3-2(-2) = 0}}}

{{{-4 + 4 = 0}}}

{{{0 = 0}}}


{{{-2x+5y+10z=-3}}} ……………………….(2)

{{{-2(-1)+5*3+10(-2) =-3}}}
	
{{{2 + 15  -20 = -3}}}

{{{ 17  -20 = -3}}}

{{{ -3  = -3}}}


{{{3x+y=0}}} ………………………………..(3)

{{{3(-1) + 3 = 0}}}

{{{-3 + 3 = 0}}}

{{{0 = 0}}}