To determine if the point [tex]\((5,6)\)[/tex] is a solution to both equations in the system, we need to check whether it satisfies each equation. Let's proceed with each step carefully.
1. Check the first equation: [tex]\(y = 2x - 4\)[/tex]
Substitute [tex]\(x = 5\)[/tex] and [tex]\(y = 6\)[/tex] into the first equation:
[tex]\[ y = 2x - 4 \][/tex]
[tex]\[ 6 = 2(5) - 4 \][/tex]
[tex]\[ 6 = 10 - 4 \][/tex]
[tex]\[ 6 = 6 \][/tex]
The equality holds true, so [tex]\((5,6)\)[/tex] satisfies the first equation.
2. Check the second equation: [tex]\(y - x = 1\)[/tex]
Substitute [tex]\(x = 5\)[/tex] and [tex]\(y = 6\)[/tex] into the second equation:
[tex]\[ y - x = 1 \][/tex]
[tex]\[ 6 - 5 = 1 \][/tex]
[tex]\[ 1 = 1 \][/tex]
The equality holds true, so [tex]\((5,6)\)[/tex] satisfies the second equation as well.
Since [tex]\((5,6)\)[/tex] satisfies both equations in the system, we can conclude that [tex]\((5,6)\)[/tex] is indeed a solution to the system of equations.
Therefore, the correct answer is:
Yes
