Question

What is the solution of the system? Use substitution.

x = –2y + 10
–6y = 6x – 6
z = –3x + 10y


A. x = 9, y = –8, z = 114

B. x = –8, y = 9, z = 114

C. x = –8, y = 114, z = 9

D. x = 114, y = 9, z = –8

Answer 1

Substitute the first equation into the second equation , solve for y

Answer 2

i dont know how to substitute

Answer 3

Okay. First obvious thing to notice is that the second equation can be simplifed to y = 1 - x (just divide by 6 on each side). We substitute the first equation into this, so we have: \[ \Large {y = 1 - x = 1 - (2y + 10) = -2y - 9}. \]So, we have a linear equation wrt y: y = -2y - 9 -> 3y = -9 -> y = -3. Thus, we have: x = 1 - y = 1 + 3 = 4. Finally, z = -3x + 10y = -3(4) + 10(-3) = -12 - 30 = -42.

Our solution is: (4, -3, 42). The choices seem to be incorrect, unless someone can find a really stupid mistake I made.

Answer 4

so what do i do

Answer 5

Do ... about ... what?

Answer 6

@Ahaanomegas , from the first two equations, I am getting y=9. Mind checking that for me?

Answer 7

Oops, that's where I made my mistake. When substituting, I used x = 2y + 10, instead of -2y + 10. Thanks for catching that, @CliffSedge (!)

Answer 8

Alright. I'm trying best to be helpful to @jennyjewell25 .
I think from getting that y=9, the rest shouldn't be too hard.