Determine the value of z for the system of equations. x + y + z = 2 3x - 2y + 2z = -8 8z - 12y - x = 12

Step-by-step explanation:

To get the value of z, we need to reduce the system of equation into two and 2 unknowns;

Add 1 and 3:

y - 12y + z + 8z = 2+12

-11y + 9z = 14 4

Also Multiply equation 1 by 3 and subtract from 2

Eqn 1 * 2 will give 3x + 3y + 3z = 6

Subtract from eqn 2;

3y-(-2y)+3z-2z = 6-(-8)

5y+z = 14 5

Solve 4 and 5

-11y + 9z = 14 * 5

5y+z = 14 * 11

-55y + 45z = 70

55y + 11z = 154

Add both

45z+11z = 70+154

56z = 224

z= 224/56

z = 4

Hence the value of z is 4

probably .5

i can on others if necessary.

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.