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