High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Which of the following equations could be the result of using the comparison method to solve the system shown?

[tex]
\begin{array}{l}
x+y=5 \\
2x+y=7
\end{array}
[/tex]

A. [tex]5-x=2x-7[/tex]

B. [tex]5-x=7-2x[/tex]

C. [tex]-x-5=7-2x[/tex]

Answer :

To solve the given system of equations using the comparison method and find which of the given equations could result from the process, follow these steps:

We are given the system:

1. [tex]\( x + y = 5 \)[/tex]
2. [tex]\( 2x + y = 7 \)[/tex]

Step 1: Express [tex]\( y \)[/tex] from the First Equation

From the first equation, [tex]\( x + y = 5 \)[/tex], we can express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:

[tex]\[ y = 5 - x \][/tex]

Step 2: Substitute [tex]\( y \)[/tex] into the Second Equation

Substitute the expression for [tex]\( y \)[/tex] into the second equation, [tex]\( 2x + y = 7 \)[/tex]:

[tex]\[ 2x + (5 - x) = 7 \][/tex]

Step 3: Simplify the New Equation

Simplify the equation obtained after substitution:

[tex]\[ 2x + 5 - x = 7 \][/tex]

Combine like terms:

[tex]\[ x + 5 = 7 \][/tex]

Step 4: Rearrange and Simplify Further

Rearranging the terms gives:

[tex]\[ x = 7 - 5 \][/tex]

Therefore:

[tex]\[ x = 2 \][/tex]

Step 5: Substitute Back to Find [tex]\( y \)[/tex]

Now, substitute [tex]\( x = 2 \)[/tex] back into the expression for [tex]\( y \)[/tex]:

[tex]\[ y = 5 - 2 = 3 \][/tex]

Step 6: Possible Resulting Comparison Equation

The goal is to find which of the given equations could result from this method. The comparison that accurately translates the steps taken is:

[tex]\[ 5 - x = 7 - 2x \][/tex]

Conclusion

Thus, the correct choice from the list provided is:

[tex]\[ 5 - x = 7 - 2x \][/tex]

This equation accurately represents what we obtained during the process when we solved for [tex]\( x \)[/tex].