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Anettt [7]
3 years ago
5

What are the solutions to the following system?

Mathematics
1 answer:
bija089 [108]3 years ago
6 0

The solutions are (\sqrt{2},-1) \text { and }(-\sqrt{2},-1).

Solution:

Given equation:

-2 x^{2}+y=-5

Add 2 x^{2} on both sides.

-2 x^{2}+y+2 x^{2}=-5+2 x^{2}

y=-5+2 x^{2} -------- (1)

y=-3 x^{2}+5 (given)  -------- (2)

Equate (1) and (2).

-5+2 x^{2}=-3 x^{2}+5

Add 3 x^{2} on both sides.

-5+2 x^{2}+3 x^{2}=-3 x^{2}+5 +3 x^{2}

-5+5x^{2}=5

Add 5 on both sides.

-5+5x^{2}+5=5+5

5x^{2}=10

Divide by 5 on both sides, we get

x^{2}=2

Taking square root on both sides, we get

x=\sqrt{2}, x=-\sqrt{2}

Substitute x=\sqrt{2} in (1).

y=-5+2(\sqrt{2})^2

y=-5+4

y=-1

Substitute x=-\sqrt{2} in (1).

y=-5+2(-\sqrt{2})^2

y=-5+4

y=-1

Therefore the solutions are (\sqrt{2},-1) \text { and }(-\sqrt{2},-1).

Option C is the correct answer.

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