solve useing addition

Question

3x-4y-2z=17

4x-3y+5Z=5

5x-5y+3Z=14

Answer 1

Elimination method : 

Given equations are

3x-4y-2z = 17  ---> (1)

4x-3y+5z = 5   ---> (2)

5x-5y+3z = 14 ---> (3)

Multiple to each side of equation (1) by 4.

3x-4y-2z = 17  ---> (1)

12x-16y-8z =68 ---> (4)

Multiple to each side of equation (2) by 3.

4x-3y+5z = 5   ---> (2)

12x-9y+15z =15 --->(5)

To eliminate the x  value subtract (5) from (4).

12x-16y-8z = 68

12x-9y+15z = 15

(-)(+)(-) (-)

__________

-7y-23z = 53 ---> (5)

Multiple to each side of equation (2) by 5.

4x-3y+5z = 5   ---> (2)

20x-15y+25z = 25----->(6)

Multiple to each side of equation (3) by 4.

5x-5y+3z = 14 ---> (3)

20x - 20y+12z = 56----->(7) To eliminate the x  value subtract (7) from (6).

20x-15y+25z = 25

20x-20y+12z = 56

(-)(+)(-) (-)

________

5y+13z = -31 ---> (8)

To eliminate the y value

Multiple to each side of equation (5) by 5.

-7y-23z = 53 ---> (5)

-35y-115z =265---->(9)

Multiple to each side of equation (8) by 7.

5y+13z = -31 ---> (8)

35y+91z = -217 ---->(10)

To eliminate the y  value add (10)&(9).

-35y-115z =265---->(9)

35y+91z = -217 ---->(10)

_________

-24z =48

z = -48/24=-2

⇒ z = -2

Put z in (8).

5y+13(-2) = -31

5y+(-26) =-31

5y =-31+26=-5

⇒ y =-1

Put y,z in (1).

3x-4(-1)-2(-2) = 17

3x +(4)+4=17

3x =17-8=9

⇒ x = 3

Solution  x = 3, y = -1, and z =-2.