Question

what is the solution to the system of equations: x- - y-z = 2, - x - 3 y - 2 z + 4, -x - 2 z = 10

Answer 1

Given equations are x- - y-z = 2, - x - 3 y - 2 z + 4, -x - 2 z = 10 .

It seems you have missed to write = in the 2nd equation so i have fixed the sign and going to solve the following system of equations:

x-y-z=2 ...(i)

-x-3y-2z=4 ...(ii)

-x-2z=10 ...(iii)

solve (i) for x

x=2+y+z ...(iv)

plug (iv) into (ii)

-x-3y-2z=4

-(2+y+z)-3y-2z=4

-2-y-z-3y-2z=4

-2-4y-3z=4

-4y-3z=6...(v)

plug (iv) into (iii)

-x-2z=10

-(2+y+z)-2z=10

-2-y-z-2z=10

-2-y-3z=10

-y=12+3z

y=-12-3z...(vi)

plug (vi) into (v)

-4y-3z=6

-4(-12-3z)-3z=6

48+12z-3z=6

48+9z=6

9z=-42

z=-14/3

Now plug value of z into (vi)

y=-12-3z=-12-3(-14/3)=-12+14=2

y=2

plug value of y and z into (iv)

x=2+y+z=2+2-14/3=-2/3

Hence final answer is x=-2/3, y=2, z=-14/3