Question

If you were to use the elimination method to solve the following system, choose the new system of equations that would result after the variable z is eliminated in the first and second equations, then the second and third equations.

x + y – 3z = –8
2x + 2y + z = 12
3x + y – z = –2


Choices:



A.x + y = –8
3x + y = –2

B.7x + 7y = 28
5x + 3y = 10

C.x + y = –8
5x + 3y = 14

D.7x + 7y = 28
3x + y = –2

Answer 1

B

Answer 2

x+y-3z=-8)*1
2x+2y+z=12)*-3 (jst to make coefficient of z equal)
=x+y-3z=-8
-6x-6y-3z=-36
+ + + +
=7x+7y= 28
similarly 2x+2y+z=12)*-1
3x+y-z=-2)*1
= -2x-2y-z=-12
3x+y-z=-2
- - +
= -5x-3y=-10
= -(5x+3y)=-10
=5x+3y=10