Discover a world of knowledge and community-driven answers at IDNLearn.com today. Our platform is designed to provide trustworthy and thorough answers to any questions you may have.

Which system of equations can be graphed to find the solution(s) to [tex]\(x^2 = 2x + 3\)[/tex]?

A. [tex]\(\left\{\begin{array}{l}y = x^2 + 2x + 3 \\ y = 2x + 3\end{array}\right.\)[/tex]
B. [tex]\(\left\{\begin{array}{l}y = x^2 - 3 \\ y = 2x + 3\end{array}\right.\)[/tex]
C. [tex]\(\left\{\begin{array}{l}y = x^2 - 2x - 3 \\ y = 2x + 3\end{array}\right.\)[/tex]
D. [tex]\(\left\{\begin{array}{l}y = x^2 \\ y = 2x + 3\end{array}\right.\)[/tex]


Sagot :

To determine which system of equations can be graphed to find the solution(s) to the equation [tex]\( x^2 = 2x + 3 \)[/tex], let's start by rewriting the given equation in a way that can help us identify the system of equations.

Given:
[tex]\[ x^2 = 2x + 3 \][/tex]

First, isolate one side of the equation to form a standard quadratic equation:
[tex]\[ x^2 - 2x - 3 = 0 \][/tex]

Now let’s consider the graphing approach. One way to graphically solve for [tex]\( x \)[/tex] is to express the original equation as two functions and see where they intersect.

Rewrite the equation in terms of two separate functions [tex]\( y \)[/tex]:
1. [tex]\( f_1(x) = x^2 \)[/tex]
2. [tex]\( f_2(x) = 2x + 3 \)[/tex]

So the system of equations becomes:
[tex]\[ \begin{cases} y = x^2 \\ y = 2x + 3 \end{cases} \][/tex]

Thus, to find the solution(s) to the equation [tex]\( x^2 = 2x + 3 \)[/tex], we can graph the following system of equations and find the points where these graphs intersect:
[tex]\[ \begin{cases} y = x^2 \\ y = 2x + 3 \end{cases} \][/tex]

This matches the last option provided:
[tex]\[ \begin{cases} y = x^2 \\ y = 2x + 3 \end{cases} \][/tex]

Therefore, the system of equations that can be graphed to find the solution(s) to [tex]\( x^2 = 2x + 3 \)[/tex] is:
[tex]\[ \begin{cases} y = x^2 \\ y = 2x + 3 \end{cases} \][/tex]