Question

Solve the following system by the method of reduction.

4x-16z=24

2x-3y-3z=25

2x+2y-3z=-5

4x+2y+2z=-6

Answer 1

x=2,y=-6,z=-1

Explanation:

Hello, I think I can help you

Let

equation 1 (1) 4x-16z=24

equation 2 (2) 2x-3y-3z=25

equation 3 (3) 2x+2y-3z=-5

equation 4 (4) 4x+2y+2z=-6

to eliminate x and z , we can do

(2)-(3)

2x-3y-3z=25

-(2x+2y-3z=-5)

____________

0-5y-0 =30

-5y=30

divide each side by -5

-5y/-5=30/-5

y=-6

to eliminate y , we can do

(3)-(4)

2x+2y-3z=-5

-(4x+2y+2z=-6)

___________

-2x+0-5z=1 equation (5)

Now, to eliminate z do, (1)+2*(5)

(1) 4x-16z=24

2*(5)=-4x-10z=2

(1)+2*(5)

4x-16z=24

-4x-10z=2

_________

0-26z=26

-26z=26

z=26/-26

z=-1

from (1) isolating x

4x-16z=24

4x=24+16z

x=6+4z

x=6+4(-1)

X=2

have a great day