Question

I really need help with this! I don't really understand linear equation stuff and I asked my teacher about it but she isn't helping. I only need help with one question. If you need anything else to answer it just tell me.

Use the system of linear equations you wrote to solve for the variables p and q. Show all work.

Here's the linear equations I wrote down:
Supply: p = 1/40q + 9.75
Demand: p = -1/50q + 12

Answer 1

The graph seems to show the solution to be the point (50, 11), and, indeed, that point checks in both equations!

To use algebra to solve the linear system, make the problem easier to solve by eliminating fractions.

Multiply all terms in the first equation by 40 (the denominator in the coefficient of q):


`40(p)=40\left((1)/(40)+9.75 \right) \\ 40p=q+390`

Multiply all terms in the second equation by 50:


`50(p)=50 \left( -(1)/(50) q+12 \right) \\ 50p=-q+600`

Add the two resulting equations.


`40p=q+390 \\ 50p=-q+600 \\ 90p = 990 \\ p=11`

Plug that back into either equation to get q=50.