Sure, let's analyze the given statements step-by-step based on the equation and the substitution:
1. Statement: "You replaced [tex]$y$[/tex] with 3 temporarily."
- This is a true statement. We are substituting [tex]\( y \)[/tex] with 3 to find the corresponding value of [tex]\( x \)[/tex].
2. Statement: "This is wrong because you can only substitute for [tex]$x$[/tex]."
- This is a false statement. In an equation, you can substitute known values for any variable, whether it is [tex]\( x \)[/tex] or [tex]\( y \)[/tex], to find the corresponding value of the other variable.
3. Statement: "The equation becomes [tex]$3=x-2$[/tex]."
- This is a true statement. By substituting [tex]\( y \)[/tex] with 3 in the equation [tex]\( y = x - 2 \)[/tex], the equation transforms to [tex]\( 3 = x - 2 \)[/tex].
4. Statement: "The value of [tex]$x$[/tex] is 5."
- This is a true statement. Solving the equation [tex]\( 3 = x - 2 \)[/tex] for [tex]\( x \)[/tex], we get:
[tex]\[
3 = x - 2 \implies x = 3 + 2 \implies x = 5
\][/tex]
5. Statement: "The equation [tex]$y=x-2$[/tex] is still true, just with specific values."
- This is a true statement. The original equation [tex]\( y = x - 2 \)[/tex] remains valid. When [tex]\( y = 3 \)[/tex] and [tex]\( x = 5 \)[/tex], the equation holds true, i.e., [tex]\( 3 = 5 - 2 \)[/tex].
To conclude, the true statements are:
- "You replaced [tex]$y$[/tex] with 3 temporarily."
- "The equation becomes [tex]$3=x-2$[/tex]."
- "The value of [tex]$x$[/tex] is 5."
- "The equation [tex]$y=x-2$[/tex] is still true, just with specific values."
DONE ✔
