X+y+z=0 (1) 2x+4y+2z=12 (2) -x+9y-3z=66 (3) solve the system of equations a single solution?(in simplified dorm) infinitely many solutions?

Question

X+y+z=0 (1) 2x+4y+2z=12 (2) -x+9y-3z=66 (3) solve the system of equations a single solution?(in simplified dorm) infinitely many solutions? or the system is inconsistent.(empty set)

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Natalia 2 months 2021-10-09T04:57:14+00:00 1 Answer 0 views 0

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    2021-10-09T04:58:58+00:00

    Answer:

    x=-3,y=6,z=-3.

    Step-by-step explanation:

    We have been given a system. We are asked to solve our given system of equations.

    x+y+z=0...(1)

    2x+4y+2z=12...(2)

    -x+9y-3z=66...(3)

    From equation (1), we will get:

    x=-y-z...(1)

    Upon substituting this value in equation (2), we will get:

    2(-y-z)+4y+2z=12\\\\ -2y-2z+4y+2z=12\\\\2y=12\\\\y=\frac{12}{2}\\\\y=6

    Upon substituting x=-y-z in equation (3), we will get:

    -(-y-z)+9y-3z=66\\\\y+z+9y-3z=66\\\\10y-2z=66\\\\10(6)-2z=66\\\\-2z=66-60\\\\-2z=6\\\\ \frac{-2z}{-2}=\frac{6}{-2}\\\\z=-3

    Let us solve for x as:

    x=-y-z\\\\ x=-6-(-3)\\\\x=-6+3\\\\x=-3

    Therefore, the solutions of our given system is x=-3,y=6,z=-3.

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