Given Information:

The system of equations is;

x+2y=42x−y=1

Graph:

Consider the equations,

x+2y=42x−y=1

Rewrite the given equations,

y=−x2+2y=2x−1

Use the graphing calculator to determine the solution of the given system of equation,

Step 1: In the TI-83 calculator press the ON key.

Step 2: Click on the Y= button.

Step 3: Write the desired equation in Y1 and Y2 as follows:

Y1=−X2+2Y2=2X−1

Step 4: Press the WINDOW button and set the window as;

Xmin=−10,Xmax=10,Xscl=5,Ymin=−5,Ymax=5,Yscl=5

Step 5: Press the GRAPH button to get the graph.

The graph is shown below;

From the graph, it can be observed that the graphs of the system of equation intersect at a single point.

Interpretation:

As the graphs of the equation intersect at a single point there is a unique solution for the given system of equation.