Question

What are the solutions to the following system?{-2x+y=-5y=-3x2 + 50 (0, 2)O (1, -2)o (12.-1) and (- 12.-1):o 15.-10) and (-75-10

Answer 1

`(\sqrt[]{2\text{ }},-1)\text{ and (-}\sqrt[]{2\text{ }}\text{ ,-1)}`

Step-by-step explanation:

Here, we want to solve the system of equations

Since we have y in both equations, let us start by rewriting the second equation to look like the first

We have that as:

`\begin{gathered} -2x^2+y\text{ = }-5 \\ y+3x^2\text{ = 5} \end{gathered}`

Subtract equation ii from i

We have it that:

`\begin{gathered} -5x^2=\text{ -10} \\ 5x^2=10 \\ x^2=\text{ 2} \\ \\ x\text{ = }\pm\sqrt[]{2} \end{gathered}`

when x = positive root 2, we have it that:

`\begin{gathered} -2x^2+y\text{ = -5} \\ -2(\sqrt[]{2\text{ }})^2+y\text{ = -5} \\ -4+y\text{ = -5} \\ y\text{ = -5+4} \\ y\text{ = -1} \end{gathered}`

when x = negative root 2:

We will still get the same answer as the square of both returns the same value

Thus, we have the solution to the system of equations as:

`(\sqrt[]{2\text{ }},-1)\text{ and (-}\sqrt[]{2\text{ }}\text{ ,-1)}`