We have been given two equations.
[tex]y=x-3[/tex] and [tex]y=x^{2}+2x-4[/tex]
When we will substitute y in one of these equation we will get
[tex]x-3=x^{2}+2x-4[/tex]
Now let us find which of the given options are equivalent to our equation.
A) [tex]x-3=x^{2}[/tex] This is not equivalent to our answer. [tex]2x-4[/tex] is missing.
B) [tex]y=(x-3)^{2}+2(x-3)-4[/tex] In this equation y's value has been substituted in place of x which will make the equation wrong. When we will substitute value of [tex]x-3[/tex] we will get [tex]y=(y)^{2}+2(y)-4[/tex] which is not true.
C) [tex]x-3=x^{2}+2x-4[/tex] is equivalent to our equation.
D) [tex]y=x^{2}+2x-4-(x-3)[/tex] In this equation [tex]x-3[/tex] is being subtracted from [tex]x^{2}+2x-4[/tex]. When we will simlify this equation we will get
[tex]y=x^{2}+2x-4+x+3=x^{2}+3x-1[/tex] This is not true and we were asked only to substitute y in our given equation.
Therefore option C is correct.
