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

Jan 29, 2018

See below...

#### Explanation:

To solve this we must graph each of the lines:

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

Rearange:

$4 y = 2 - 2 x$

$\implies y = \frac{1}{2} - \frac{1}{2} x$

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

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

At $x = 1$ , $y = \frac{1}{2} - \left(\frac{1}{2} \cdot 1\right) = \frac{1}{2} - \frac{1}{2} = 0$

At $x = - 1$ , $y = \frac{1}{2} - \left(\frac{1}{2} \cdot - 1\right) = \frac{1}{2} + \frac{1}{2} = 1$

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:

$\textcolor{red}{\underline{\text{They are the same line! }}}$

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