You are looking for the solution to the given equations by graphing them.
First you need to create a table of values. Using these values the given lines can be graphed. From the graph, the solution can be determined.
First equation is: [tex]y= \frac{1}{2}x+3 [/tex]
Using different values of x, we can find corresponding y values which can be used to graph the line.
For x=0, [tex]y= \frac{1}{2}(0)+3=3 [/tex]
For x=2, [tex]y= \frac{1}{2}(2)+3=4 [/tex]
For x=4, [tex]y= \frac{1}{2}(4)+3=5 [/tex]
For x=6, [tex]y= \frac{1}{2}(6)+3=6 [/tex]
Second equation is:
[tex]-3x+y=-2 \\ \\
y=3x-2[/tex]
Using different values of x, we can find corresponding y values which can be used to graph the line.
For x = 0, [tex]y=3(0)-2=-2[/tex]
For x = 2, [tex]y=3(0)-2=4[/tex]
For x = 3, [tex]y=3(0)-2=7[/tex]
For x = 1, [tex]y=3(0)-2=1[/tex]
We can see that the value of y is same for both the lines at x = 2. So (2,4) is the solution of the equations. This can also be observed from the graph by plotting these lines as shown in the image below
