Question

Question #b0e8c

Answer 1

You must solve this system of equations by substitution.

Explanation:

This problem looks really bad when you look at it. However, many times in mathematics, things that look bad really are not when you use basic principles.

Here we have a system of equations where the variables are already solved, The Y, C, &, I. This means it is set up perfectly for substitution.

We are going to take the equation:
`Y = C + I`
and substitute the `C` for the `a+bY` and `I` for the `u+vY`

here is what that looks like:
`Y= (a+bY) + (u+vY)`

solve for Y by moving all the Y to one side:
`Y = a+bY+u+vY`
`Y-bY-vY = a+u`

factor out the Y and you get:
`Y(1-b-v)=a+u`

then divide by the `(1-b-v)`:
`Y=(a+u)/(1-b-v)`

this is the solution for the total value of the economy in terms of just the constants. It really wasn't that hard and that makes us happy!
:)