Question

2x+y +z=0
x + 2y-z=0
6x+ 3y +3z=0​

Answer 1

Answer:

Step-by-step explanation:

3x +2y − z = − 1

− 2x − 2y +3z = 5 We will eliminate y using two different pairs of equations

5x +2y − z = 3

1

3x +2y − z = − 1 Using the first two equations,

− 2x − 2y +3z = 5 Add the first two equations

(A) x +2z = 4 This is equation (A), our first equation

− 2x − 2y +3z = 5 Using the second two equations

5x +2y − z = 3 Add the second two equations

(B) 3x +2z = 8 This is equation (B), our second equation

(A) x +2z = 4 Using (A) and (B) we will solve this system.

(B) 3x +2z = 8 We will solve by addition

− 1(x +2z) =(4)( − 1) Multiply (A) by − 1

− x − 2z = − 4

− x − 2z = − 4 Add to the second equation, unchanged

3x +2z = 8

2x = 4 Solve, divide by 2

2 2

x = 2 We now have x! Plug this into either(A) or(B)

(2) +2z = 4 We plug it into (A),solve this equation,subtract 2

− 2 − 2

2z = 2 Divide by 2

2 2

z = 1 We now have z! Plug this and x into any original equation

3(2) +2y − (1)= − 1 We use the first, multiply 3(2) =6 and combine with − 1

2y + 5= − 1 Solve,subtract 5

− 5 − 5

2y = − 6 Divide by 2

2 2

y = − 3 We now have y!

(2, − 3, 1) Our Solution

As we are solving for x, y, and z we will have an ordered triplet (x, y, z) instead of