Question

How do you solve the system by graphing `2x + 4y =2` and `x + 2y = 1`?

Answer 1

See below...

Explanation:

To solve this we must graph each of the lines:

First line: `2x+4y=2`

Rearange:

`4y = 2 - 2x`

`=> y = 1/2 - 1/2x`

Now we need to plot two or three points that lie on the line:

We need to find `y` at some `x` values:

At `x = 1` , `y = 1/2 - (1/2*1)= 1/2 - 1/2 = 0`

At `x = -1` , `y = 1/2 - (1/2*-1) = 1/2 +1/2 = 1`

Hence these are two points that lie on the line:

`color(blue)( (1,0)` and `color(red)( (-1,1)`

Hence connecting them up to give a line:

Now we can do this whole procces for the second line, graphing them on the same graph we see:

`color(red)( underline( "They are the same line! " ) )`

When we deal with these roblems, the solution is where the lines intersect, where they meet

They meet at all points, as they are the same:

`color(red)("The solutions to this system is all the points that lie on"`
`color(red)(-> 2x+4y=2`