y = -x^2 + 13
x^2 + y^2 = 25
1. (4,-3), (-4,-3)
2. (4,-3), (3,4), (-3,4), (-4,-3)
3. (9,94), (16,269)
4. (3,4), (-3,4)
Please help!!
2007-04-30 16:24:25 · 4 answers · asked by JamesA 1 in Science & Mathematics ➔ Mathematics
by substitution
2007-04-30 16:30:58 · update #1
y = -x^2 + 13
x^2 + y^2 = 25
Substitute
x^2 + (13 - x^2)^2 = 25
x^2 + 169 - 26x^2 + x^4 = 25
Combine line terms, arrange in descending order
x^4 - 25x^2 + 144 = 0
Factor
(x^2 - 16 )(x^2 - 9) = 0
(x + 4)(x - 4)(x + 3)(x - 3) = 0
Set factors equal to zero and solve
x + 4 = 0
x = -4
x - 4 = 0
x = 4
x + 3 = 0
x = -3
x - 3 = 0
x = 3
Substitute each value of x into one of the equations to find y.
(4, -3) (3, 4), (-3, 4), (-4, -3)
(all of these work in x^2 + y^2 = 25)
2007-04-30 16:36:41 · answer #1 · answered by suesysgoddess 6 · 1⤊ 0⤋
3
2007-04-30 23:32:20 · answer #2 · answered by ¼ + ½ = ¾ 3 · 0⤊ 0⤋
x^2 = 13 - y
=> y^2 - y + 13 = 25
=> y^2 - y -12 = 0
=> y^2 - 4y + 3y - 12 = 0
=> (y-4)(y+3) = 0
=> y = -3, 4
x = sqrt(13 - y)
Substituting, x = +/-4 (if y = -3) or +/-3 (if y = 4)
Ans: 2
2007-05-01 00:17:49 · answer #3 · answered by SB 1 · 0⤊ 0⤋
What exactly are you trying to do here?
2007-04-30 23:30:01 · answer #4 · answered by bruinfan 7 · 0⤊ 0⤋