Answer:
C: k=-2
Step-by-step explanation:
Eq 1: [tex]x^{2}[/tex]-6x+9=0
Eq 2: x+k=1
Solve Eq 2 for x:
x=1-k
Sub x into Eq 1:
[tex](1-k)^{2}[/tex]-6(1-k)+9=0
Solve for k:
[tex]k^{2}[/tex]-2k+1-6+6k+9=0
[tex]k^{2}[/tex]+4k+4=0
Factor:
[tex](k+2)^{2}[/tex]=0
Square root both sides:
k+2=0
k=-2
