Math Help!!
posted by Sara on .
Solve
2xy5z=1
x+2y+3z=9
3x+6y+z=11
2x3y=13
5x+2y=16

1. Eq1: 2x y  5z = 1.
Eq2: x + 2y + 3z = 9.
Eq3: 3x + 6y + z = 11.
Multiply Eq1 by 3 and Eq2 by 5:
6x  3y 15z = 3
5x + 10y + 15z = 45
Add Eq1 and Eq2:
Eq4: 11x + 7y = 48
Eq2: x + 2y + 3z = 9
Multiply Eq3 by 3:
Eq3: 9x  18y  3z = 33
Add Eq2 and Eq3 and get:
Eq5: 8x  16y = 24
Eq5: x  2y = 3
Eq4: 11x + 7y = 48
Eq5: x  2y = 3.
Multiply Eq5 by 11 and add to Eq4:
Eq5: 11x  22y = 33
15y = 15
Y = 1.
In Eq5, substitute 1 for y:
x  2*(1) = 3
x + 2 = 3
x = 5
X = 5.
In Eq1, sub. 5 for X and 1 for Y:
2*5  (1)  5z = 1
10 + 1  5z = 1
5z = 1  11 = 10
Z = 2.
Solution set = (x,y,z) = (5,1,2).
2. Eq1: 2x  3y = 13.
Eq2: 5x + 2y = 16.
Multiply Eq1 by 5 and Eq2 by 2:
10x  15y = 65.
10x + 4y = 32.
Add the 2 Eqs:
11y = 33
Y = 3.
In Eq1, substitute 3 for Y:
2x  3*3 = 13
2x = 13 + 9 = 4
X = 2.
Solution set = (2,3).