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].
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].
