Math stuff its a SOE

Question

2x-y+z=-2

x+2y+2z=3

2x- 2y+z=0

Those are all togther i think its called a system of equation

Answer 1

Hi Mabry,

Yes, it's a system of 3 equations.

You can solve it by using graphs, substitutions, or eliminations, but for now, I will use eliminations.

Even in eliminations, there are multiple ways to do it too.

To make it easier, I will name each equation (A), (B), and (C).

2x - y + z = -2 ...... (A)

x + 2y + 2z = 3 ...... (B)

2x - 2y + z = 0 ...... (C)

(A) - (C):

2x - y + z = -2

-(2x - 2y + z = 0)

y = -2

Substitute y = -2:

(A): 2x - (-2) + z = -2

2x + z = -4 ........... (A')

(B): x + 2(-2) + 2z = 3

x + 2z = 7 ............. (B')

(C): 2x - 2(-2) + z = 0

2x + z = -4 ........... (C')

(A') - 2(B'):

2x + z = -4

-(2x + 4z = 14)

-3z = - 18

z = 6

Substitute y = -2 and z = 6 into (A) and solve for x:

2x - (-2) + 6 = -2

2x + 8 = -2

2x = - 10

x = -5

Double check:

2x - y + z = 2(-5) - (-2) + 6 = -10 + 2 + 6 = -2 check

x + 2y + 2z = -5 + 2(-2) + 2(6) = -5 - 4 + 12 = 3 check

2x - 2y + z = 2(-5) - 2(-2) + 6 = -10 + 4 + 6 = 0 check

Therefore, x = -5, y = -2, z = 6