What is the result of substituting for $y$ in the bottom equation?

[tex]
\begin{array}{l}
y=x-3 \\
y=x^2+2 x-4
\end{array}
[/tex]

A. [tex]$y=x^2+2 x-4-(x-3)$[/tex]
B. [tex]$y=(x-3)^2+2(x-3)-4$[/tex]
C. [tex]$(x-3)=x^2$[/tex]
D. [tex]$x-3=x^2+2 x-4$[/tex]

Substitute x − 3 for y in the equation y = x 2 + 2 x − 4 .
This yields x − 3 = x 2 + 2 x − 4 .
Compare the result with the given options.
The correct answer is x − 3 = x 2 + 2 x − 4 ​ .

Explanation

Understanding the Problem We are given two equations:

y = x − 3
y = x 2 + 2 x − 4
We are asked to substitute the first equation into the second equation for the variable y .

Performing the Substitution To substitute y = x − 3 into the second equation y = x 2 + 2 x − 4 , we replace y in the second equation with the expression x − 3 . This gives us:

x − 3 = x 2 + 2 x − 4
Now we compare this result with the given options.

Identifying the Correct Option Comparing our result x − 3 = x 2 + 2 x − 4 with the given options:


Option A: y = x 2 + 2 x − 4 − ( x − 3 ) is incorrect because it subtracts ( x − 3 ) from the right side.
Option B: y = ( x − 3 ) 2 + 2 ( x − 3 ) − 4 is incorrect because it substitutes ( x − 3 ) for x instead of y .
Option C: ( x − 3 ) = x 2 is incorrect because it doesn't include the 2 x and − 4 terms.
Option D: x − 3 = x 2 + 2 x − 4 is the correct result of the substitution.


Final Answer The result of substituting y = x − 3 into the equation y = x 2 + 2 x − 4 is:

x − 3 = x 2 + 2 x − 4
Therefore, the correct answer is D.
Examples
Substitution is a fundamental technique in algebra, used to solve systems of equations and simplify expressions. For instance, in physics, if you know the velocity of an object as a function of time, v ( t ) , and you also know the position as a function of velocity, x ( v ) , you can substitute v ( t ) into x ( v ) to find the position as a function of time, x ( t ) . This allows you to describe the object's motion completely in terms of time.

Answered by GinnyAnswer | 2025-07-08