Question

tell whether the ordered pair \\(\left(5, 2\frac{1}{2}\
ight)\\) is a solution of the system of linear equations \\(y = x - 2\frac{1}{2}\\) and \\(y = -\frac{1}{2}x + 5\\). \\(\left(5, 2\frac{1}{2}\
ight)\\) \\(\boxed{}\\) a solution of the system of linear equations.

Explanation:

Step1: Check first equation

Substitute \( x = 5 \) and \( y = 2\frac{1}{2}=\frac{5}{2} \) into \( y=x - 2\frac{1}{2} \).
Right - hand side: \( 5-2\frac{1}{2}=5-\frac{5}{2}=\frac{10 - 5}{2}=\frac{5}{2} \), which equals \( y \).

Step2: Check second equation

Substitute \( x = 5 \) and \( y=\frac{5}{2} \) into \( y =-\frac{1}{2}x + 5 \).
Right - hand side: \( -\frac{1}{2}(5)+5=-\frac{5}{2}+\frac{10}{2}=\frac{5}{2} \), which equals \( y \).

Answer:

is