Question

Use a both elimination and substitution to solve this system of linear equations. Type your answer as an ordered triplet, like this: (-2, 4, 13)

2x−10y+1=z
4x + y = z + 18
-2x - 8z = y - 1

Answer 1

Ok, lets start by solving one of the equations for one of the variables.

Which variable would you like to start with?

Answer 2

the first set

Answer 3

If I said a good place to start would be the variable z, why do you think that would be a good idea?

Answer 4

cause its easiest?

Answer 5

Right! It's already solved for.
2x−10y+1 = z
z = 2x−10y+1

Ok so we know what z is equal too.

Let's use this information to plug substitute what we got for z into one of the other equations.

Answer 6

The second equation has z by itself in there.

Let's plug in 2x−10y+1 for z since z = 2x−10y+1

We would get from
4x + y = z + 18
To
4x + y = (2x - 10y +1) +18
Right?

Do you have any questions so far?

Answer 7

not so far

Answer 8

Actually I'm making this harder than it needs to be.

Let's actually solve for y in the second equation since it is by itself.
4x + y = z + 18

Comes to y = -4x + z + 18
Right?

So we have,
z = 2x−10y+1
y = -4x + z + 18

Answer 9

The order of steps can really make things complicated or easy depending on which route you take. The way I was doing it would have worked but would have been a nightmare to work through haha.

Answer 10

Are you with me so far? When you are, we can continue.