Question

How do i solve this by using elimination method?

3y-5z=-23

4x+2y+3z=7

-2x-y-z=-3


I need help on this!step by step explanations would be really helpful!

Answer 1

y=-6, x=4, z=1

Explanation:

1st step

3y-5z=-23

4x+2y+3z=7

-2x-y-z=-3

2nd step

4x+2 * -23+5z/3 +3z=7

-2x- -23+5z/3 -z=-3

3rd step

4x+ -46+19z/3 =7

-2x+ 23-8z/3 =-3

4th step

-2 * -19z+67/12 + 23-8z/3 =-3

5th step

z-7/ 2 =-3

6th step

x= -19 1+67/12

x=4

7th step

-23+5z/3 Substitute x=4, z=1 y=-6

Answer 2

Answer: x=4 y=-6 z=1

Explanation:

`3y-5z=-23 \ \ \ \ \ \ \ \ (1)\\4x+2y+3z=7\ \ \ \ \ (2)\\-2x-y-z=-3\ \ \ (3)\\\\`

Multiply the equation (3) by 2:

`-4x-2y-2z=-6\ \ \ \ \ (4)\\`

Sum the equations (2) and (4):

`4x+2y+3z=7\\-4x-2y-2z=-6\\\\z=1`

Substitute the value of z into equation (1):

`3y-5(1)=-23\\3y-5=-23\\3y-5+5=-23+5\\3y=-18`

Divide both parts of the equation by 3:

`y=-6`

Thus,

`-2x-(-6)-1=-3\\-2x+6-1=3\\-2x+5=-3\\-2x+5-5=-3-5\\-2x=-8`

Divide both parts of the equation by -2:

`x=4`