How do you solve the system of equations algebraically #x-3z=7, 2x+y-2z=11, -x-2y+9z=13#?
1 Answer
Explanation:
Write out the three equations to line up the unknown values. This will give you a clue how to proceed.
Always be careful of the signs
# x -3z = 7 #
#2x +y -2z = 11#
# -x -2y +9z = 13#
Already we can see that it is easy to solve for
#x -3z = 7 >> x = 3z +7#
Insert the value for
#2(3z +7) +y -2z = 11#
#6z +14 + -2z = 11#
#4z +y = -3#
#y = -4z -3#
Substitute the values of
#-(3z+7) -2(-4z-3) +9z = 13#
#-3z -7 +8z +6 +9z = 13#
#14z = 14#
#z = 1#
Substitute the value of
#x -3(1) = 7#
#x = 10#
Substitute the values of
#2(10) +y -2(1) = 11#
#20 +y -2 = 11#
#y = -20 +2 +11#
#y = -7#
Use either equation that includes all three unknowns to check:
#-x -2y +9z = 13#
#-(10) -2(-7) +9(1) = 13#
#13 = 13#