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)![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=4a57d162627345c40a6d32d67881a7ac.png\")
12x-16y-8z =68 ---> (4)
\Multiple to each side of equation (2) by 3.
\4x-3y+5z = 5 ---> (2)![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=eda826ec0f3a0891ad36d2acc78100a3.png\")
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)![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=e88429dddd1ac39acc5f53761dc68a44.png\")
20x-15y+25z = 25----->(6)
\Multiple to each side of equation (3) by 4.
\5x-5y+3z = 14 ---> (3)![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=4a57d162627345c40a6d32d67881a7ac.png\")
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)![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=e88429dddd1ac39acc5f53761dc68a44.png\")
-35y-115z =265---->(9)
\Multiple to each side of equation (8) by 7.
\5y+13z = -31 ---> (8)![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=5c17b3710f3ce0d02b4c7c58a158dfe8.png\")
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.
\