Answered

IDNLearn.com: Where your questions meet expert advice and community support. Discover reliable and timely information on any topic from our network of experienced professionals.

The first two steps in determining the solution set of the system of equations, [tex]$y = x^2 - 6x + 12$[/tex] and [tex]$y = 2x - 4$[/tex], algebraically are shown in the table.

\begin{tabular}{|c|c|}
\hline
Step & Equation \\
\hline
Step 1 & [tex]$x^2 - 6x + 12 = 2x - 4$[/tex] \\
\hline
Step 2 & [tex][tex]$x^2 - 8x + 16 = 0$[/tex][/tex] \\
\hline
\end{tabular}

Which represents the solution(s) of this system of equations?

A. [tex]$(4, 4)$[/tex]

B. [tex]$(-4, -12)$[/tex]

C. [tex][tex]$(4, 4)$[/tex][/tex] and [tex]$(-4, 12)$[/tex]

D. [tex]$(-4, 4)$[/tex] and [tex][tex]$(4, 12)$[/tex][/tex]

Sagot :

GinnyAnsweridn
To solve the system of equations
[tex]\[ y = x^2 - 6x + 12 \][/tex]
and
[tex]\[ y = 2x - 4, \][/tex]
we follow these steps:

1. Set the equations equal to each other to eliminate [tex]\( y \)[/tex]:
[tex]\[ x^2 - 6x + 12 = 2x - 4 \][/tex]

2. Move all terms to one side to form a quadratic equation:
[tex]\[ x^2 - 6x + 12 - 2x + 4 = 0 \][/tex]
Simplifying this, we get:
[tex]\[ x^2 - 8x + 16 = 0 \][/tex]

3. Factor or solve the quadratic equation:
[tex]\[ x^2 - 8x + 16 = 0 \][/tex]
This can be factored as:
[tex]\[ (x - 4)^2 = 0 \][/tex]
Therefore, we have a double root:
[tex]\[ x = 4 \][/tex]

4. Substitute the value of [tex]\( x \)[/tex] back into one of the original equations to find [tex]\( y \)[/tex]. Using [tex]\( y = 2x - 4 \)[/tex]:
[tex]\[ y = 2(4) - 4 = 8 - 4 = 4 \][/tex]

Hence, the solution to the system of equations is:
[tex]\[ (4, 4) \][/tex]

Thus, the correct answer is:
[tex]\[ (4, 4) \][/tex]
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.