Math question! 10 POINTS best answer!!!

find the solutions to the equations
equations:
x+4y-5z=-8
x+4y-4z=-2
x+5y-4z=3

possible answers:
A. x=3 y=14 z=-12
B. x=2 y=4 z=5
C. x=4 y=5 z=6
D. x=2 y=5 z=6

plz help an xplain if possible how u did it thax!

First, take equations 1) and 2) and solve for one variable

x+4y-5z = -8 same sign before x and y, so subtract bottom equation from top
x+4y-4z = -2

This gives z = 6

Plug value for z into equation 3)

x+5y-4(6) = 3
x+5y-24 = 3
x+5y = 3+24
x+5y = 27

Plug value for z into equation 1)

x+4y-5(6) = -8
x+4y-30 = -8
x+4y = -8+30
x+4y = 22

Now take the two equations you have created and solve for one variable.

x+4y = 22
x+5y = 27

This gives y = 5

Now plug this value into one of these two equations.

x+4(5) = 22
x+20 = 22
x =22-20
This gives x = 2

So, D. x = 2 y =5 z = 6

Hope this helps.

OK

x + 4y -5z = -8
x + 4y -4z = -2
x +5y -4z = 3

Take the first two equations, and subtract the second from the first - you get

-z = -6
So z = 6 (already you know that A and B are incorrect)

Now take the second and third equation and subtract the third from the second - you get
-y = - 5
So y = 5 ( both C and D have this, so we are not done yet).

Finally, take the two answers and plug into one of the equations

x + 4(5) - 5(6) = -8
x + 20 -30 = -8
x -10 = -8
x = 2

SO === D is the answer.

Prove it by placing the answers in a different equation ( I used the first one, so this time I will use the second)

2 + 4(5) - 4(6) = -2??
2 +20-24 = -2??
-2 = -2 YES!!

Hope that helps.

the second and third equation are the same except for the extra y and the difference is 5 so y is 5
the first and second are the same except for the extra z so z is 6