Question

How is the line graphed and how do we determine the solution?

Answer 1

No solution

Step-by-step explanation:

Given the system

`\begin{gathered} -x+2y=4 \\ y=(1)/(2)x+3 \end{gathered}`

Graph the first equation -x+2y = 4.

Identify two points on the line. Plot and join them to get the graph of the line.

When x = 0, y =2. First point is (0, 2).

When y = 0, x = -4. Second point is (-4, 0).

Now, graph the second equation y= (1/2)x+3.

Identify two points on the line. Plot and join them to get the graph.

When x = 0, y = 3. First point is (0, 3).

When y = 0, x = -6. Second point is (-6, 0).

The graph of both lines are parallel, that is, not intersecting anywhere. Hence the system has no solution.