Substitution and Evaluation

[fg9]

I'm understanding upto the red doodle point. How are we "combining" after that? Can someone work it out for me?

 

[Otis]

… Can someone work it out for me?

Hi fg9. There are different ways to express both X₁ and X₂ in terms of P₁ and P₂. Your subject line implies that you tried the substitution method. Can you show your attempt (up to the point where you got stuck)?

If you weren't able to start, then here's one way to carry out the substitutions. Solve the following for X₂ (let's call it equation #1):

\[X_1 = \frac{m - P_2 \cdot X_2}{P_1} \quad (1)\]

Your result will take this form (let's call it equation #3):

\[X_2 = \text{expression containing X}_1 \quad (3) \]

We'll use equation #3, at the end. Next, solve the following for X₂ (let's call it equation #2):

\[\frac{X_2 + 3}{X_1 + 2} = \frac{P_1}{P_2} \quad (2)\]

You've now solved both equations #1 and #2 for X₂. Set those results equal to one another, and solve that equation for X₁. The solution will match the final expression given for X₁.

The last steps are to substitute the final expression for X₁ into equation #3 and to solve that for X₂. The solution will match the final expression given for X₂.

Again, these steps are just one of several ways to express X₁ and X₂ each in terms of P₁ and P₂. If you tried something else, and you want to go that route, then please show us your steps. Otherwise, try the approach above, and let us know if you have any questions.

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