lovelycharm
  • lovelycharm
What are the x-coordinates of the solutions to this system of equations? x2 + y2 = 16 y = x + 4
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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Vocaloid
  • Vocaloid
do a substitution y = x + 4 means we can replace "y" with "x + 4" when we see y, so x^2 + y^2 = 16 x^2 + (x+4)^2 = 16 know where to go from here?
lovelycharm
  • lovelycharm
then u divide the by 4
Vocaloid
  • Vocaloid
uhhhh not quite

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Vocaloid
  • Vocaloid
then we can use FOIL to expand (x+4)^2
lovelycharm
  • lovelycharm
2x+8
Vocaloid
  • Vocaloid
not quite, the ^2 is an exponent (x+4)^2 = (x+4)(x+4) = ?
lovelycharm
  • lovelycharm
0
Vocaloid
  • Vocaloid
nope, not quite... hint: (x+A)(x+A) = x^2 + 2*A*x + A^2 (x+4)(x+4) = ____________________ fill in the blank
lovelycharm
  • lovelycharm
x+4x+4x+16
Vocaloid
  • Vocaloid
almost, you're very close! x^2 + 4x + 4x + 16
Vocaloid
  • Vocaloid
that simplifies to: x^2 + 8x + 16, with me so far?
lovelycharm
  • lovelycharm
2x+8x+16 4x+16
Vocaloid
  • Vocaloid
nope, not quite. please remember that x^2 is NOT equal to 2x
Vocaloid
  • Vocaloid
x^2 means x*x, ok?
lovelycharm
  • lovelycharm
so it was x+8x+16
lovelycharm
  • lovelycharm
confuse
Vocaloid
  • Vocaloid
yes, x^2 + 8x + 16, with me so far?
lovelycharm
  • lovelycharm
x+4^2
Vocaloid
  • Vocaloid
no, we just leave it as x^2 + 8x + 16, ok?
lovelycharm
  • lovelycharm
What are the x-coordinates of the solutions to this system of equations? x2 + y2 = 16 y = x + 4 −4 and 0 4 and 0 −2 and −3 2 and −3
lovelycharm
  • lovelycharm
those r the option
Vocaloid
  • Vocaloid
right, we'll get to that in a minute, ok?
Vocaloid
  • Vocaloid
right now we have: (x+4)^2 = x^2 + 8x + 16 plugging that back into the first equation gives us x^2 + x^2 + 8x + 16 = 16 know where to go from here?
lovelycharm
  • lovelycharm
no not really
Vocaloid
  • Vocaloid
start by subtracting 16 from each side.
lovelycharm
  • lovelycharm
0
Vocaloid
  • Vocaloid
what about the left side? x^2 + x^2 + 8x + 16 - 16 = ?
lovelycharm
  • lovelycharm
4
Vocaloid
  • Vocaloid
nope, maybe this will make things easier: (x^2 + x^2 + 8x) + 16 - 16 = ?
lovelycharm
  • lovelycharm
8x^2+0
lovelycharm
  • lovelycharm
2x^2+8x
Vocaloid
  • Vocaloid
good, 2x^2 + 8x
Vocaloid
  • Vocaloid
now we have 2x^2 + 8x = 0 solve for x
lovelycharm
  • lovelycharm
4x+8x=0 4x=0
Vocaloid
  • Vocaloid
remember what I said earlier? x^2 is NOT 2x
Vocaloid
  • Vocaloid
2x^2 + 8x = 0 2x(x+4) = 0 solve for x
lovelycharm
  • lovelycharm
2x2+8x
Vocaloid
  • Vocaloid
not quite... 2x^2 + 8x is what I gave you to start with
Vocaloid
  • Vocaloid
2x = 0 x = ?
lovelycharm
  • lovelycharm
4
Vocaloid
  • Vocaloid
try again
Vocaloid
  • Vocaloid
2x = 0 divide both sides by 2
lovelycharm
  • lovelycharm
0
Vocaloid
  • Vocaloid
good
Vocaloid
  • Vocaloid
now we solve (x+4) = 0 x = ?
lovelycharm
  • lovelycharm
4
Vocaloid
  • Vocaloid
almost but not quite
Vocaloid
  • Vocaloid
subtract 4 from each side
lovelycharm
  • lovelycharm
-4
Vocaloid
  • Vocaloid
good, so our solutions are 0 and -4
lovelycharm
  • lovelycharm
thank u so much

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