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Alinara [238K]
3 years ago
11

Use substitution to solve the following system of linear equations and fill in the following blanks:

Mathematics
1 answer:
marissa [1.9K]3 years ago
6 0

Answer:

x=-4

y=3

z=-5

Step-by-step explanation:

<u>Given:</u>

x+y+z=-6

x-6y-7z=-29

-7y-5z=4

<u>Solve for </u>x<u> in the 1st equation:</u>

x+y+z=-6

x+y=-z-6

x=-y-z-6

<u>Substitute the value of </u>x<u> into the 2nd equation and solve for </u>z<u>:</u>

x-6y-7z=-29

(-y-z-6)-6y-7=-29

-7y-z-13=-29

-7y-z=-16

-z=-16+7y

z=16-7y

<u>Substitute the value of </u>z<u> into the 3rd equation and solve for </u>y<u>:</u>

-7y-5z=4

-7y-5(16-7y)=4

-7y-80+35y=4

28y-80=4

28y=84

y=3

<u>Plug </u>y=3<u> into the solved expression for </u>z<u> and evaluate to solve for </u>z<u>:</u>

z=16-7(3)

z=16-21

z=-5

<u>Plug </u>z=-5<u> into the solved expression for </u>x<u> and evaluate to solve for </u>x<u>:</u>

x=-(3)-(-5)-6

x=-3+5-6

x=2-6

x=-4

Therefore:

x=-4

y=3

z=-5

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