Let's determine if [tex]\( x = 2 \)[/tex] and [tex]\( y = 3 \)[/tex] are solutions to the simultaneous equations [tex]\( x + y = 5 \)[/tex] and [tex]\( x - y = 1 \)[/tex].
1. Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 3 \)[/tex] into the first equation [tex]\( x + y = 5 \)[/tex]:
[tex]\[
x + y = 2 + 3
\][/tex]
Simplifying the left-hand side, we get:
[tex]\[
2 + 3 = 5
\][/tex]
This is indeed equal to 5. Thus, the first equation is satisfied.
2. Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 3 \)[/tex] into the second equation [tex]\( x - y = 1 \)[/tex]:
[tex]\[
x - y = 2 - 3
\][/tex]
Simplifying the left-hand side, we get:
[tex]\[
2 - 3 = -1
\][/tex]
This simplifies to [tex]\(-1\)[/tex], which does not equal 1. Thus, the second equation is not satisfied.
Therefore, while [tex]\( x = 2 \)[/tex] and [tex]\( y = 3 \)[/tex] satisfy the first equation, they do not satisfy the second equation. Hence, [tex]\( x = 2 \)[/tex] and [tex]\( y = 3 \)[/tex] are not the correct solutions to the simultaneous equations [tex]\( x + y = 5 \)[/tex] and [tex]\( x - y = 1 \)[/tex].
