Answer:
A. If a=−3 and b=4 , then there is exactly one solution to the equation.
C. If a=9 and b=−2 , then there is no solution to the equation.
Step-by-step explanation:
The given equation is
[tex]3(3x+4)-5=ax+b[/tex]
To solve for [tex]x[/tex], we need to use the distributive property
[tex]3(3x+4)-5=ax+b\\9x+12-5=ax+b\\9x-ax=b-7\\x(9-a)=b-7[/tex]
To find the right statement, we need to the given values.
For a=-3 and b=4,
[tex]x(9-a)=b-7\\x(9-(-3))=4-7\\x(9+3)=-3\\12x=-3\\x=\frac{-3}{12} =-\frac{1}{4}[/tex]
So, choice A is true, because there's one solution to the equation.
For a=-9 and b=13,
[tex]x(9-a)=b-7\\x(9-(-9))=13-7\\18x=6\\x=\frac{6}{18}=\frac{1}{3}[/tex]
The choice B is false.
For a=9 and b=-2
[tex]x(9-a)=b-7\\x(9-9)=-2-7\\0x=-9\\0=-9[/tex]
Choice C is correct, because there's no solution, because zero is not equal to -9.
For a=-3 and b=-5
[tex]x(9-a)=b-7\\x(9-(-3))=-5-7\\12x=-12\\x=\frac{-12}{12}=-1[/tex]
Choice D is false, becuase there's only one solution.
For a=9 and b=7
[tex]x(9-a)=b-7\\x(9-9)=7-7\\0x=0\\0=0[/tex]
Choice E is false, because there are infinite solutions in ths case.
Therefore, the right choices are A and C.
