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!