What are the solutions of the following system? -2x^2 + y=-5 y=-3x^2+5

Mathematics

2 answers:

Ray Of Light [21]2 years ago

8 0

Answer:

Step-by-step explanation:

Doss [256]2 years ago

5 0

$\begin{cases}-2x^2+y=-5\\y=-3x^2+5\end{cases}\\\\\\
-2x^2+(-3x^2+5)=-5\\\\
-2x^2-3x^2+5=-5\quad|-5\\\\-5x^2=-10\quad|:(-5)\\\\x^2=2\\\\
\boxed{x=-\sqrt{2}\qquad\vee\qquad x=\sqrt{2}}\\\\\\
y=-3x^2+5\qquad\vee\qquad y=-3x^2+5\\\\
y=-3(-\sqrt{2})^2+5\qquad\vee\qquad y=-3(\sqrt{2})^2+5\\\\
y=-3\cdot2+5\qquad\vee\qquad y=-3\cdot 2+5\\\\
y=-6+5\qquad\vee\qquad y=-6+5\\\\
\boxed{y=-1\qquad\vee\qquad y=-1}\\\\\\
\begin{cases}x=-\sqrt{2}\\y=-1\end{cases}\qquad\vee\qquad\begin{cases}x=\sqrt{2}\\y=-1\end{cases}$

Answer C.

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Hi student, let me help you out! :)

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We are asked to find the equation of the line, using the given information:

$\star~\mathrm{-3}$ , which is the slope

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$\triangle~\fbox{\bf{KEY:}}$

The slope is the number before x, in the form $\mathtt{y=mx+b}$ .

Since "m" is the slope, and we're given what the slope is, we can substitute -3 for m:

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Now, we need to find the y intercept, "b", of the line.

Here's how it's done:

Remember the point that the line contains, (1,2)?

Well, its y-coordinate is 2; so what we do is substitute 2 for y:

$\dag~\mathtt{2=-3x+b}$