How do you solve x+3y-z=13, 2x-5z=23, 4x-y-2z=14?
1 Answer
#x=366/114#
#y=738/342#
#z=(-189)/57#
Explanation:
#x+3y-z=13# ------------------(1)
#2x-5z=23# ------------------(2)
#4x-y-2z=14# ----------------(3)
Solve equations (1) and (2)
#x+3y-z=13# ------------------(1)
#2x-5z=23# ------------------(2)
Multiply equation (1) with
#x+3y-z=13 xx 2# ------------------(1)
#2x+0y-5z=23# ------------------(2)
#2x+6y-2z=26 # ------------------(1) Subtract (2) from (1)
#2x+0y-5z=23# ------------------(2)
# 6y+3z=3# ----------------(4)
Solve equations (2) and (3) and eliminate
#2x+0y-5z=23# ------------------(2)
#4x-y-2z=14# ----------------(3)
Multiply (2) with
#2x+0y-5z=23 xx 2# ------------------(2)
#4x-y-2z=14# ----------------(3)
#4x+0y-10z=46# ------------------(2) Subtract (3) from (2)
#4x-y-2z=14# ----------------(3)
#y-8z=32# ----------------(5)
Take equations (4) and (5)
#6y+3z=3# ----------------(4)
#y-8z=32# ----------------(5)
Multiply equation (5) with
#6y+3z=3# ----------------(4) Subtract (5) from (4)
#6y-54z=192# ----------------(5)
#57z=-189#
#z=(-189)/57#
Substitute the value of
#2x-5z=23# ------------------(2)
#2x-5((-189)/57)=23# ------------------(2)
#2x+945/57=23# ------------------(2) Multiply both sides by#57#
#114x+945=1311# -------- Solve it for#x#
#114x=1311-945=366#
#x=366/114#
Substitute the value of
#x+3y-z=13# ------------------(1)
#366/114+3y-(-189)/57=13#
#366/114+3y+189/57=13# ---- Multiply both sides with#114#
#366+342y+378=1482# -------solve it for#y#
#744+342y=1482#
#342y=1482-744=738#
#y=738/342#