Precalculus, Chapter 7, 7.3, Section 7.3, Problem 36

(1) 2x-2y-6z=-4
(2) -3x+2y+6z=1
(3) x-y-5z=-3

Use equations (1) and (2) to eliminate the y and z variables.
(1) 2x-2y-6z=-4
(2) -3x+2y+6z=1
___________________
-x=-3

x=3

Divide equation (1) by a -2. Use equations (1) and (3) to eliminate the x and y variables.
(1) -x+y+3z=2
(3) x-y-5z=-3
________________
-2z=-1

z=1/2

Solve for y by substituting the x and z variables in to equation (3).
(3) x-y-5z=-3
(3)-y-5(1/2)=-3
3-y-(5/2)=-3
y=3-(5/2)+3
y=7/2

The solution set for the given system of equations is (3, 7/2, 1/2).


Check your answer by substituting the values for x, y, and z in the given equations.
(1) 2x-2y-6z=-4
2(3)-2(7/2)-6(1/2)=-4
6-7-3=-4
-4=-4

(2) -3x+2y+6z=1
-3(3)+2(7/2)+6(1/2)=1
-9+7+3=1
1=1

(3) x-y-5z=-3
3-(7/2)-5(1/2)=-3
3-(7/2)-(5/2)=-3
-3=-3