SOLUTION: Quesion: Choose the nonlinear systesm below that have (x,y) = (4,3) as on of their solutions. (a) x^2+y^2=25 x+y=7 (b) y=x^2+2x-21 x-y+1 (c) x^2-y^2=7 2x+y=

Algebra ->  College  -> Linear Algebra -> SOLUTION: Quesion: Choose the nonlinear systesm below that have (x,y) = (4,3) as on of their solutions. (a) x^2+y^2=25 x+y=7 (b) y=x^2+2x-21 x-y+1 (c) x^2-y^2=7 2x+y=      Log On


   

Question 30337: Quesion: Choose the nonlinear systesm below that have (x,y) = (4,3) as on of their solutions.
(a) x^2+y^2=25
x+y=7
(b) y=x^2+2x-21
x-y+1
(c) x^2-y^2=7
2x+y=9
(d) a and b
(e) b and c
Answer by sdmmadam@yahoo.com(530) About Me  (Show Source):
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Quesion: Choose the nonlinear systesm below that have (x,y) = (4,3) as on of their solutions.
(a) x^2+y^2=25
x+y=7
(b) y=x^2+2x-21
x-y+1
(c) x^2-y^2=7
2x+y=9
(d) a and b
(e) b and c

(a) x^2+y^2=25
x+y=7
x= 4 and y = 3 gives
x^2+y^2 =4^2+3^2 = 16+9 = 25
and x+y = 4+3= 7
Therefore (a) holds for x = 4 and y =3
(b) y=x^2+2x-21
x-y=1
x= 4 and y = 3 gives
x^2+2x-21 = 4^2+2X(4)-21 = 16+8-21=3 = y
x-y = 4-3 = 1
Therefore (b) holds for x = 4 and y =3

(c) x^2-y^2=7
2x+y=9
x= 4 and y = 3 gives
x^2-y^2= 4^2-3^2 = 16-9 = 7
2x+y = 2X4 +3 = 8+3 = 11 NOT EQUAL TO the given 9
Therefore (c) DOES NOT HOLD for x = 4 and y =3
Since both (a) and (b) hold
therefore the choice (d) a and b
is the right answer