High School

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].