What is the solution to the system of equations? 2x-3y+z=-19 5x+y-z=-7 -x+6y-z=35 a. (2,-6,-11) b. (-2,6,3) c. (6,2,-25) d. (-2,6,9)

that answer is B because first u have to solve for Z in 2x-3y+Z=19

Z will be Z=-19-2x+3y

B. (-2,6,3)

Step-by-step explanation:

First we will cancel the z-variable in the first two equations.  We will do this by adding the second equation to the first:

Next we cancel the z-variable in the bottom two equations.  We will do this by subtracting the bottom equation from the middle one:

We can now take these equations without z as a system:

We will make the coefficients of y the same by multiplying the top equation by 5 and the bottom by 2:

Next we subtract the bottom equation from the top:

Divide both sides by 23:

23x/23 = -46/23

x = -2

Substitute this into the first equation without z:

7(-2)-2y = -26

-14-2y = -26

Add 14 to each side:

-14-2y+14 = -26+14

-2y = -12

Divide both sides by -2:

-2y/-2 = -12/-2

y = 6

Substitute both x and y into our first original equation:

2(-2)-3(6)+z = -19

-4-18+z = -19

-22+z = -19

Add 22 to each side:

-22+z+22 = -19+22

z = 3

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