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Posted by **Sara** on Thursday, May 17, 2012 at 6:26pm.

2x-y-5z=1

x+2y+3z=9

3x+6y+z=11

2x-3y=-13

-5x+2y=16

- Math Help!! -
**Henry**, Friday, May 18, 2012 at 5:24pm1. 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).