Solve the system.

3x2 - 2y2 = -5
x2 + y2 = 25
A. (3, 4), (3, -4), (-3, 4), (-3, -4)
B. (4, 4), (5, 4), (3, -4), (1, –4)
C. (-3, 4), (1, 4), (-3, -4), (2, -4)
D. (1, 4), (2, –4), (–4, 3), (–3, –3)

Find the coordinates of the corner points using the following:

x - y = -2
2x + y = -1
x = -2
A. (-2, 0)
B. (-2, 0), (-1, 1)
C. (-2, 0), (-1, 1), (-2, 3)
D. (-1, 1), (-2, 3)

i choose 1. b

2. C

#1 and did you actually try using your choices to see whether they worked?

You know that if ((x,y) is a solution, so is (-x,-y) since both x^2 and y^2 are the same value whether x,y are positive or negative.

Double eq #2 and add it to eq #1 to get 5x^2 = 45, so x^2 = 9.

So, x = ±3
Then, thinking back to the good ole 3-4-5 right triangle, you can see that y= ±4.

So, (A) is the answer.

#2. correct

thank you

To solve the first system of equations:

1. Start by using the second equation to solve for x^2: x^2 = 25 - y^2.
2. Substitute x^2 in the first equation, giving you: 3(25 - y^2) - 2y^2 = -5.
3. Simplify and rearrange the equation: 75 - 3y^2 - 2y^2 = -5.
4. Combine like terms: 75 - 5y^2 = -5.
5. Move -5 to the left side of the equation: 5y^2 = 80.
6. Divide both sides of the equation by 5: y^2 = 16.
7. Take the square root of both sides: y = ±4.
8. Substitute the values of y back into the second equation to solve for x: x^2 + 16 = 25.
9. Simplify: x^2 = 9.
10. Take the square root of both sides: x = ±3.
11. Therefore, the coordinates of the intersection points are: (3, 4), (3, -4), (-3, 4), (-3, -4).

Therefore, the correct answer is A.

To solve the second system of equations:

1. We are given the equation x = -2.
2. Substitute x = -2 into the first equation: -2 - y = -2.
3. Simplify and rearrange the equation: -y = 0.
4. Divide both sides of the equation by -1: y = 0.
5. Therefore, the coordinates of the corner point are (-2, 0).
6. The second equation is not needed to find the coordinates of the corner points.

Therefore, the correct answer is A.