Question

How do you use the graphing method to solve `2x+4y=8, 3x+6y=12`?

Answer 1

See explanation.

Explanation:

Our task is manipulate both equations into the slope-intercept form. Then, we can graph both linear functions and see where they intersect (their intersection(s) = the solutions of the equations). Let's start with the equation `2x+4y=8`:

`2x+4y=8`

`4y=8-2x`

`y=(8-2x)/4`

`color(red)y=8/4-(2x)/4=2-1/2x=color(red)(-1/2x+2)`

Onto the second equation:

`3x+6y=12`

`6y=12-3x`

`y=(12-3x)/6`

`color(blue)y=12/6-(3x)/6=2-1/2x=-color(blue)(1/2x+2)`

The two equations, when simplified, are the same equation! And that means that they are the same line. Since the two lines are the same line, that means they have an infinite number of solutions.

Now, I will show you the graph of both of these lines (I will be only showing you one because both lines' graphs are identical):

graph{y=-1/2x+2 [-10.25, 9.75, -2.6, 7.4]}

Hope I helped!
- ILuvGaming101