what are the values of x and z in the solution system of linear equations below? -3x-2y+4z = -16 10x+10y-5z=30 5x+7y+8z=-21

first thing, take 3 pairs of equations and in each pair, make any one variable's coefficient equal to the coefficient of the same variable in the other equation and subtract the equations.

you will get 3 different equations:  

x+y = 1

- 4x - 21z = 72

-x + 3z = -10 (simplified)

now take the value of x and y from equation 2 and 3 in terms of z and substitute x and y with those values

y = (72 + 21z)/-4

x = 3z + 10

as x + y = 1

you will get z = -4 after sloving the equation

now you have the value of one of the variables..

now we will substitute z in the equations to get the other variables

x = 3z + 10

x = 3(-4) + 10

x = -12 + 10

x = -2  

Now y:

72+21(-4)/-4

(72 - 84)/-4

-12/-4

y  = 3

so,

z = -4

x = -3

y = 3

I assume that it's enough

x= -2, z= -4

Step-by-step explanation:

-3x-2y+4z = -16

10x+10y-5z=30 ⇒ 2x+2y-z=6 ⇒ 14x+14y-7z=42

5x+7y+8z=-21 ⇒ 10x+14y+16z= -42

Add up the first one with the second:

-3x-2y+4z = -16

+

2x+2y-z=6

-x+3z= -10 ⇒ x= 3z+10

Subtract the last one from the second:

14x+14y-7z=42

-

10x+14y+16z= -42

Replace x with 3z+10