[tex]$x=2$[/tex] and [tex]$y=3$[/tex] are the solutions to the simultaneous equations [tex]$x+y=5$[/tex] and [tex]$x-y=1$[/tex].

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25-07-2024
Mathematics

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[tex]$x=2$[/tex] and [tex]$y=3$[/tex] are the solutions to the simultaneous equations [tex]$x+y=5$[/tex] and [tex]$x-y=1$[/tex].

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-07-25T18:03:02-04:00

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].