+0

Help. ​

0
307
3

Help. Jan 11, 2018

#1
0

x + y   =   3     subtract  x  from both sides to get     y  =  3 - x

x2 + y2   =   9       Substitute  3 - x  for  y  in this equation.

x2 + (3 - x)2   =   9               Now we can solve this for  x .

x2 + (3 - x)(3 - x)   =   9

x2 + 9 - 6x + x2   =   9          Subtract  9  from both sides and combine like terms.

2x2 - 6x   =   0                      Factor  x  out of both terms on the left side.

x(2x - 6)   =   0                     Set each factor equal to zero.

x  =  0          or          2x - 6  =  0

x  =  3

Now we can use these values for  x  to find  y .

If   x = 0 ,     0 + y = 3    so    y = 3

If   x = 3 ,     3 + y = 3    so    y = 0

The solutions are   (0, 3)   and   (3, 0) .

Jan 11, 2018
#2
+1

y  =  (x - 2)(x - 3)(x + 3)

The zeros of this are the  x  values that make  y  be zero, that is, the  x  values when

0  =  (x - 2)(x - 3)(x + 3)

Set each factor equal to zero and solve each for  x  .

x  - 2  =  0     so     x  =  2

x  - 3  =  0     so     x  =  3

x + 3  =  0     so     x  =  -3

The zeros are  2, 3, -3

Jan 11, 2018
#3
+1

Thanks, hectictar.....I messed that first one up earlier...!!!   Jan 11, 2018
edited by CPhill  Jan 11, 2018