How do you solve the system $-4x-5y-z=18$ , $-2x-5y-2z=12$ , and $-2x+5y+2z=4$ ?

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How do you solve the system $-4x-5y-z=18$ , $-2x-5y-2z=12$ , and $-2x+5y+2z=4$ ?

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Answer 1 · 2017-03-18T22:00:18

${x=-4,y=0,z=-2}$

Explanation:

$-4x-5y-z=18" , "(1)$

$-2x-5y-2z=12" , "(2)$

$-2x+5y+2z=4" , "(3)$

$"let us sum the equations numbered as (2) and (3) so as to eliminate"$

$"the terms named 'y' and 'z'".$

$-2xcancel(-5y)cancel(-2z)-2xcancel(+5y)cancel(+2z)=12+4$

$"rearrange the equation above."$

$-2x-2x=12+4$

$-4x=16" , "x=-4$

$"let us write as x=4 in the equation numbered as (1)"$

$-4(-4)-5y-z=18$

$16-5y-z=18$

$-5y-z=18-16$

$-5y-z=2" , "(4)$

$"let us write as x=4 in the equation numbered as (2)"$

$-2(-4)-5y-2z=12$

$8-5y-2z=12$

$-5y-2z=12-8$

$-5y-2z=4" , "(5)$

$"now , subtract (5) from (4) "$

$-5y-z-(-5y-2z)=2-4$

$cancel(-5y)-z cancel(+5y)+2z=-2$

$-z+2z=-2$

$z=-2"$

$"now use (4)"$

$-5y-(-2)=2$

$-5y+2=2$

$-5y=0$

$y=0$

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How do you solve the system $-4x-5y-z=18$ , $-2x-5y-2z=12$ , and $-2x+5y+2z=4$ ?

1 Answer

Explanation:

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How do you solve the system -4x-5y-z=18-4x-5y-z=18, -2x-5y-2z=12-2x-5y-2z=12, and -2x+5y+2z=4-2x+5y+2z=4?

1 Answer

Explanation:

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How do you solve the system $-4x-5y-z=18$ , $-2x-5y-2z=12$ , and $-2x+5y+2z=4$ ?