Question

Solve the system by elimination

-2x + 2y + 3z = 0
-2x - y + z = -3
2x + 3y + 3z = 5

Answer 1

- 2 x + 2 y + 3 z = 0 Multiply both sides by - 1

2 x - 2 y - 3 z = 0


- 2 x + 2 y + 3 z = 0
+
2 x + 3 y + 3 z = 5
_________________

5 y + 6 z = 5


2 x - 2 y - 3 z = 0
+
- 2 x - y + z = - 3
__________________

- 3 y - 2 z = - 3 Multiply both sides by 3

- 9 y - 6 z = - 9


- 9 y - 6 z = - 9
+
5 y + 6 z = 5
___________________

- 9 y + 5 y - 6 z + 6 z = - 9 + 5

- 4 y = - 4 Divide both sides by - 4

- 4 y / - 4 = - 4 / - 4

y = 1

Replace this value in equation 5 y + 6 z = 5

5 y + 6 z = 5

5 * 1 + 6 z = 5

5 + 6 z = 5 Subtract 5 to both sides

5 + 6 z - 5 = 5 - 5

6 z = 0 Divide both sides by 6

z = 0


Replace y = 1 and z = 0 in equation 2 x + 3 y + 3 z = 5

2 x + 3 y + 3 z = 5

2 x + 3 * 1 + 3 * 0 = 5

2 x + 3 + 0 = 5

2 x + 3 = 5 Subtract 3 to both sides

2 x + 3 - 3 = 5 - 3

2 x = 2 Divide both sides by 2

x = 1


The solutions are:

x = 1

y = 1

z = 0

Answer 2

this is correct

Answer 3

Thanks bro

Answer 4

5x+4y=1 3x+4y=-7 elimination

Answer 5

Ok i get everything except why you multiplied both sides by -1 and 3.. like what made you make that decision? why is that what made the equation right?