Question

Solve the system by elimination-
{-2x+2y+3z=0
{-2x-y+z=-3
{2x+3y+3z=5
Can somebody answer this step by step or help me figure it out?

Answer 1

Take the first two equations....
-2x + 2y + 3z = 0
-2x - y + z = -3 -->(-1)-2x - y + z = - 3
----------------
-2x + 2y + 3z = 0
2x + y - z = 3 (result of multiplying by -1)
----------------add
0 + 3y + 2z = 3
3y + 2z = 3

now take the last two equations (you have to eliminate the x's)
-2x - y + z = - 3
2x + 3y + 3z = 5
----------------add
0 + 2y + 4z = 2
2y + 4z = 2

now take the answers you got an eliminate a variable
3y + 2z = 3 -->(-2)3y + 2z = 3
2y + 4z = 2
-----------
-6y - 4z = - 6 (result of multiplying by -2)
2y + 4z = 2
-----------add
-4y = - 4
-4y/-4 = -4/-4
y = 1

now sub 1 in for y in either of the equations with two variables
3y + 2z = 3
3(1) + 2z = 3
3 + 2z = 3
2z = 3 - 3
2z = 0
z = 0/2 = 0

now sub known variables into any of the original equations
2x + 3y + 3z = 5
2x + 3(1) + 3(0) = 5
2x + 3 + 0 = 5
2x = 5 - 3
2x = 2
x = 1

now lets check...
-2x + 2y + 3z = 0
-2(1) + 2(1) + 3(0) = 0
-2 + 2 + 0 = 0
0 = 0 (correct)

lets double check...
-2x - y + z = -3
-2(1) - 1 + 0 = - 3
-2 - 1 + 0 = - 3
-3 = - 3 (correct)

x = 1, y = 1, z = 0......(1,1,0)

Do you have any questions ?

Answer 2

Thank you sooo much...too bad I gave up and skipped the question :/ but thank you!

Answer 3

its not a problem........its not that hard, just time consuming....lol