Answer:
and 
Step-by-step explanation:
The first system is
and 
We substitute x=-3 and y=-3
and 
Both equations are not satisfied
The next system is
and 
We substitute x=-3 and y=-3
and 
Both equations are satisfied
The next system is
and 
We substitute x=-3 and y=-3
and 
Both equations are not satisfied
The next system is
and 
We substitute x=-3 and y=-3
and 
Both equations are not satisfied
Answer:
dx/dy = (x^4 - 2x^5y - 6xy^2) / (5x^4y^2 - 4x^3y + 2y^3).
Step-by-step explanation:
x^5y^2 − x^4y + 2xy^3 = 0
Applying the Product and Chain Rules:
y^2*5x^4*dx/dy + 2y*x^5 - (y*4x^3*dx/dy + x^4) + (y^3* 2*dx/dy + 3y^2*2x) =0
Separating the terms with derivatives:
y^2*5x^4*dx/dy - y*4x^3*dx/dy + y^3* 2*dx/dy = x^4 - 2y*x^5 - 3y^2*2x
dx/dy = (x^4 - 2x^5y - 6xy^2) / (5x^4y^2 - 4x^3y + 2y^3)
The price of 1 hat is $ 5 and price of 1 t-shirt is $ 8
<em><u>Solution:</u></em>
Let "s" be the price of 1 shirt
Let "h" be the price of 1 hat
<em><u>Given that Jones buys 7 t-shirts and 6 hats for $86</u></em>
Therefore, we can frame a equation as:
price of 1 shirt x 7 + price of 1 hat x 6 = 86

7s + 6h = 86 ------ eqn 1
<em><u>Also given that The price of each t shirt is $3 more than the price of each hat</u></em>
price of 1 shirt = 3 + price of 1 hat
s = 3 + h -------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
Substitute eqn 2 in eqn 1
7( 3 + h ) + 6h = 86
21 + 7h + 6h = 86
21 + 13h = 86
13h = 86 - 21
13h = 65
<h3>h = 5</h3>
From eqn 2,
s = 3 + h = 3 + 5 = 8
<h3>s = 8</h3>
Thus price of 1 hat is $ 5 and price of 1 t-shirt is $ 8