You have to use implicit derivative
dy / dx = y'
xy^3+y=3x
y^3 + 3xy^2 y' + y' = 3
[3xy^2 + 1) y'= 3 - y^3
3 - y^3
y' = ----------------- <-----------answer
3xy^2 + 1
Substitution
y = 2x - 12
y = -x + 3
-x + 3 = 2x - 12
+ x + x
-----------------------------
3 = 3x - 12
+ 12 + 12
-----------------------
15 = 3x
------ ------
3 3
x = 5
y = 2(5) - 12
y = 10 - 12
y = -2
The final answer is (5,-2).
Consider the example
(3x+5) - (x-10)
When we subtract off the (x-10), we are basically subtracting off x and also subtracting off -10. This is the same as adding on 10 because -(-10) = 10
So we would have these steps
(3x+5)-(x-10)
3x+5-x+10
2x+15
Often students forget to distribute the negative all the way through and would have 3x+5-x-10 as an incorrect step. You need to multiply that -1 through to each term, so that's why the distributive property is used.
1.) 3p
2. -b+3
3. 6x
4. -3p
5. -4v
6. r
7. 9-4r
8. 4b+2
9. 14n
10. 4b+2
11. 35n+45
12. -82v
13. 38n
14. 38x
Use a conversion factor and turn pounds to ounces. 1 pound = 16 ounces so
