I need help on math?! Show work please! Thank you!?

Question

solve the following system over the real number

2x^2 + 6x + 5y + 1 = 0

2x + y + 3 = 0

Answer 1

For the first one:

x = 3

y = -11

For the second one:

x = 2

y = -1

Answer 2

solve the following system over the real number

2x^2 + 6x + 5y + 1 = 0

2x + y + 3 = 0

Jade L here it is

2x² + 6x + 5y + 1 = 0 ← eq 1

2x  + y + 3 = 0 ← eq 2

Multiply eq 2 by (-5) then add to eq 1

........-10x  - 5y - 15 = 0

2x².......... + 5y + 1 = 0

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2x² - 10x - 14 = 0

x² - 5x - 7 = 0

Quadratic

a=1  b=(-5)  c=(-7)

x = -b ±√b² -4(a)(c)]/(a)

x= [5 ±√25 + 28]/2

x= [5 ±√53]/2

x= [5 ± 7.28]/2

x+ = [5 + 7.28]/2

x+ = 6.14

x- = [5 - 7.28]/2

x- = - 1.14

2x + y = -3

2(-1.14) + y = -3

y = -3/2(-1.14)

y = 3/2.28

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Ans:: x = 6.14  &  -1.14  y = 3/2.24

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hope this helps