Let #2x-y+3z=7# 1st equation
Let #5x-4y-2z=3# 2nd equation
Let #4x+y-2z=-4# 3rd equation
Use 3rd equation so that #y# in terms of #x# and #z#
#y=-4+2z-4x# 3rd equation
Use now 1st and 3rd
#2x-y+3z=7# 1st equation
#2x-(-4+2z-4x)+3z=7#
#2x+4-2z+4x+3z=7#
#2x+4x-2z+3z=7-4#
#6x+z=3# Let this be the 4th equation
Use 2nd and 3rd equations:
#5x-4y-2z=3# 2nd equation
#5x-4(-4+2z-4x)-2z=3#
#5x+16-8z+16x-2z=3#
#5x+16x-8z-2z=3-16#
#21x-10z=-13# Let this be the 5th equation
Solve for #x# and #z# using 4th and 5th equations
From 4th equation: #z=3-6x# insert in 5th equation
#21x-10z=-13# 5th equation
#21x-10(3-6x)=-13#
#21x-30+60x=-13#
#81x=30-13#
#81x=17#
#x=17/81#
Go back to the 4th equation , use #x=17/81#
From 4th equation: #z=3-6x#
#z=3-6*17/81#
#z=47/27#
Go back to the 3rd equation and use #x=17/81# and #z=47/27#
#y=-4+2z-4x# 3rd equation
#y=-4+2*47/27-4*17/81#
#y=-110/81#
The solution set:
#x=17/81#
#y=-110/81#
#z=47/27#
have a nice day from the Philippines!
