Question

Find the solution to the system of equations.

X + 4y- 5z = -6
X + 4y-4z=-2
X + 5y-4z= 1
O A. x = 2, y = 4, z = 5
O B. x = 2, y = 3, z= 4
O C. x = 5, y = 11, z = -12
O D. x= 5, y = 5, z= 3

Answer 1

B

Explanation:

First you are going to have to solve for one of the variables in the terms of the other two. The easiest one of these to start with is x.

If you take the first equation, x+4y-5z=-6 and solve for x you get

x=5z-4y-6

Now you can plug that into another equation and solve for another one of the variables. Lets use equation #2. Plugging in the definition of x into the equation you get;

(5z-4y-6)+4y-4z=-2

Simplify

z-6=-2

Conveniently, the y terms cancelled out. And therefore we know

z=4

(From there, we can determine that B is the right answer because it is the only one that gives z=4. I will walk you through the rest of the answer though)

Taking our new value of z, we can pug that value into our original x equation yielding;

x=20-4y-6

simplify

x=14-4y

Using this information, we can plug it into equation #3

(14-4y)+5y-16=1

simplify

y-2=1

solve

y=3

Now we just plug the new values of y and z into the first equation to get the value of x.

x+12-20=-6

simplify

x-8=-6

solve

x=2

Therefore;

x=2

y=3

z=4