Question

Show all your work please help me

Answer 1

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:
`y= (1)/(2)x+3`

Using different values of x, we can find corresponding y values which can be used to graph the line.

For x=0,
`y= (1)/(2)(0)+3=3`
For x=2,
`y= (1)/(2)(2)+3=4`
For x=4,
`y= (1)/(2)(4)+3=5`
For x=6,
`y= (1)/(2)(6)+3=6`

Second equation is:


`-3x+y=-2 \\ \\ y=3x-2`

Using different values of x, we can find corresponding y values which can be used to graph the line.

For x = 0,
`y=3(0)-2=-2`
For x = 2,
`y=3(0)-2=4`
For x = 3,
`y=3(0)-2=7`
For x = 1,
`y=3(0)-2=1`

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