Question

graph the system of equations to determine the solution.
$y = \frac{1}{2}x + 3$
$2y = x + 6$
use the graphing tool to graph the system.
click to enlarge graph

Explanation:

Step1: Simplify the second equation

Divide $2y = x + 6$ by 2:
$\frac{2y}{2} = \frac{x}{2} + \frac{6}{2}$
$y = \frac{1}{2}x + 3$

Step2: Compare the two equations

Both equations simplify to $y = \frac{1}{2}x + 3$, so they represent the same line.

Step3: Identify solution type

When two equations are identical, every point on the line is a solution.

Answer:

All points on the line $y = \frac{1}{2}x + 3$ are solutions; the system has infinitely many solutions.