Question

Solve the system by substitution.

-x - y - z =-8
-4x + 4y + 5z = 7
2x + 2z = 4

Answer 1

well take the last equation and make z the subject...

what you you get..?

Answer 2

z=2-x

Answer 3

Can you tell me if I am heading in the right direction?

Substitute z into equation 2.

-4x+4y+5(2-x)=7
-4x+4y+10-x=7
-4x+4y-x=-3
-3x+4y=-3

Answer 4

yes and you also need to make the substitution into the 1st equation...

Answer 5

Wait, so where do I go from where I left off? Do I solve for x or y?

Answer 6

what you will end up with is 2 equations in 2 unknowns....

if z = 2 - x

then in equation 1 you will have

-x - y -(2 -x) = -8

so

-x -y -2 + x = 8

simplifying, x will go

-y = 10

so y = -10

now make 2 substitutions into the 2nd equation

-4x +4(-10) +5(2 - x) = 7

which simplifies to

-9x -30 = 7

solve for x.

then substitute into the last equation to find z

Answer 7

Thank you. I appreciate your help. :)

Answer 8

I got -4.1 for x? Is it okay that it is a decimal?

Answer 9

There was an error in your work... You had positive 8 when it should have been negative 8. I figured it out though. Thanks!

Answer 10

well I think x is closer to -4.2 repeater...

this is an add question, in that the solutions aren't integers... and its about the 5 times I've seen it in the past fortnight.

but ignoring the answers I hope the method makes sense... thats the important part