Math Problem. Help and Show Steps? Thank you (:

Solve for X, Y, and Z.

X + Z = 7
2Y - Z = -3
-X - 3Y + 2Z = 11

X + Z = 7 ... eqn. 1
2Y - Z = -3 ...eqn. 2
-X - 3Y + 2Z = 11 ...eqn.3

Add equation 1 and 3
---> -3Y + 3Z = 18
---> -Y + Z = 6 (multiply by 2)
---> -2Y + 2Z = 12 ...eqn. 4

Add equation 4 to equation 3
---> -2Y + 2Z + 2Y - Z = 9
Z = 9

Sub Z = 9 into equation 1
--> X + 9 = 7
X = -2

Sub Z = 9 into equation 2
--> 2Y - 9 = -3
2Y = 6
Y = 3

Therefore X = -2, Y = 3, Z = 9.

I will go through substitution for you.

x + z = 7
x = 7 - z

2y - z = -3
y = (z - 3)/2

Now all you have to do is substitute these variables into your third equation and solve for z.

-x - 3y + 2z = 11
-(7 - z) - (3/2)(z - 3) + 2z = 11
z - 7 - (3/2)(z - 3) + 2z = 11
2z - 14 - 3(z - 3) + 4z = 11
6z - 14 - 3z + 9 = 11
3z = 16
z = 16/3

Now you can substitute z back into your other two equations to solve for x and y. If you do, your answer is:

x = 5/3
y = 7/6
z = 16/3

x + z = 7
2y - z = -3
-x - 3y + 2z = 11

x = 7 - z

2y - z = -3
-7 + z - 3y + 2z = 11

2y - z = -3
-y + z = 6

z = 3 + 2y

-y + (3 + 2y) = 6
y = 3

z = 3 + 2(3) = 9

x = 7 - z
x = 7 - 9 = -2

(x, y, z) = (-2, 3, 9)