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iris [78.8K]
3 years ago
14

Solve the system of equations by substitution. What is the solution for x? (1 point)

Mathematics
1 answer:
stepan [7]3 years ago
3 0

Answer:

No Solution

Step-by-step explanation:

2x + y = 1

y = 1 - 2x

4x + 2(1 - 2x) = -2

4x +2 - 4x = -2

2 = -2

The statement is false, therefore there is no solution.

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fredd [130]

\dfrac{\partial\left(2xy^4+\frac1{x+y^2}\right)}{\partial y}=8xy^3-\dfrac{2y}{(x+y^2)^2}

\dfrac{\partial\left(4x^2y^3+\frac{2y}{x+y^2}\right)}{\partial x}=8xy^3-\dfrac{2y}{(x+y^2)^2}

so the ODE is indeed exact and there is a solution of the form F(x,y)=C. We have

\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)

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so

\boxed{x^2y^3+\ln(x+y^2)=8+\ln9}

8 0
3 years ago
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