Alg2
posted by Sira .
Solve the system for z.
2x  y + 2z = 11
x  2y  3z = 5
3x + z = 3

 3 x + z =  3 Add 3 x to both sides
 3 x + 3 x + z =  3 + 3 x
z = 3 x  3
x  2 y  3 z =  5
x  2 y  3 * ( 3 x  3
) =  5
x  2 y  3 * 3 x  3 * (  3 =  5
x  2 y  9 x + 9 =  5
 8 x  2 y + 9 =  5 Add 8 x  9 to both sides
 8 x  2 y + 9 + 8 x  9 =  5 + 8 x  9
 2 y =  14 + 8 x Divide both sides by  2
y =  14 /  2 + 8 x /  2
y = 7  4 x
2 x  y + 2 z = 11
2 x  ( 7  4 x ) + 2 * ( 3 x  3 ) = 11
2 x  7 + 4 x + 6 x  6 = 11
12 x  13 = 11 Add 13 to both sides
12 x  13 + 13 = 11 + 13
12 x = 24 Divide both sides by 12
x = 24 / 12
x = 2
y = 7  4 x
y = 7  4 * 2
y = 7  8
y =  1
z = 3 x  3
z = 3 * 2  3
z = 6  3
z = 3
Solution :
x = 2 , y =  1 , z = 3