Question

tell whether the ordered pair (2, 5) is a solution of the system of linear equations.
$y = \frac{1}{2}x + 4$
$y = 2x + 1$

Explanation:

Step1: Check first equation

Substitute \(x = 2\), \(y = 5\) into \(y=\frac{1}{2}x + 4\).
Right - hand side (RHS): \(\frac{1}{2}(2)+4=1 + 4=5\).
Left - hand side (LHS): \(y = 5\). So, LHS = RHS for the first equation.

Step2: Check second equation

Substitute \(x = 2\), \(y = 5\) into \(y = 2x+1\).
RHS: \(2(2)+1=4 + 1=5\).
LHS: \(y = 5\). So, LHS = RHS for the second equation.

Answer:

Since the ordered pair \((2,5)\) satisfies both equations in the system, \((2,5)\) is a solution of the system of linear equations.