Solve

Question

2x-y-5z=1
x+2y+3z=9
3x+6y+z=11

2x-3y=-13
-5x+2y=16

Answer 1

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).