To solve the equation [tex]\( y = 5 + y \)[/tex], let's go through the steps together:
1. Isolate the variable on one side of the equation:
- We start with the equation:
[tex]\[
y = 5 + y
\][/tex]
2. Subtract [tex]\( y \)[/tex] from both sides to eliminate [tex]\( y \)[/tex] on the right-hand side:
- Subtracting [tex]\( y \)[/tex] from both sides gives:
[tex]\[
y - y = 5 + y - y
\][/tex]
3. Simplify both sides of the equation:
- On the left-hand side, [tex]\( y - y \)[/tex] simplifies to 0.
- On the right-hand side, [tex]\( 5 + y - y \)[/tex] also simplifies to 5, because the [tex]\( y \)[/tex] terms cancel each other out.
[tex]\[
0 = 5
\][/tex]
4. Analyze the resulting equation:
- The simplified equation now reads [tex]\( 0 = 5 \)[/tex].
- This is a contradiction because 0 is not equal to 5.
Given this contradiction, we conclude that there is no value of [tex]\( y \)[/tex] that can satisfy the original equation [tex]\( y = 5 + y \)[/tex]. Therefore, the equation has no solution.
