Question

HELP PLEASE: Show all steps.
solve the system by substitution.
-x-y-z=-8
-4x-4y+5z=7
2x+2z=4

Answer 1

divide the last equation by 2

and you get x + z = 2

looking at the 1st equation you get

-(x + z) -y = -8

substituting and you get

-(2) -y = -8

solve for y

Answer 2

Do I have to get Y alone in order to solve for Y?

Answer 3

yep... just add 2 to both sides of the equation 1st

then divide both sides by -1

Answer 4

y=4?

Answer 5

well I thought y = 6

but the next step is to substitute y into equation 2

-4x -24 + 5z = 7

or

-4x + 5z = 31

Answer 6

Yeah it would be 6 I did my math wrong. i was dividing -8 by 2 instead of adding 2 so it would be 6

Answer 7

ok... so that the last equation again

make z the subject

2z = 4 - 2x

divide by 2

z = 4 - 2x

substitute it into the equation

-4x + 5(4 - 2x) = 31

and solve for x

Answer 8

-6x+9=31
subtract 9 from both sides then divide by -6 to get -3.7 i feel like i did this all wrong?

Answer 9

ok... well just checking it... it does have factional answers... and y = 6 is correct

I just realised a mistake

if you substitute you are solving

-4x +5(2 - x) = 31


now

-4x + 10 - 5x = 31

or

-9x + 10 = 31

-9x = 21

x = -7/3