# How do you solve x+2y=2 and 2x+4y=4?

Mar 24, 2015

This sistem is indeterminate because the second equation is the first multiplied by $2$.

Mar 24, 2015

$x + 2 y = 2$ and $2 x + 4 y = 4$

Whether you try to solve by substitution or by addition/subtraction, you will eventually get $0 = 0$

This tells us that any solution to one equation is also a solution to the other. (The equations are equivalent.) There are other ways to see the same thing:
One equation is simply a multiple of the other.
Though of as equations on lines, the lines coincide.
In slope intercept form, both lines are: $y = - \frac{1}{2} x + 1$.

The solutions to the system are exactly the solutions of the equation. (In a sense, there is really only one equation.)

The solution set can be written in various ways. Here are some of them:

$\text{All " (x,y) " with } x + 2 y = 2$

$\text{All } \left(x , 1 - \frac{1}{2} x\right)$

$\text{All } \left(- 2 y + 2 , x\right)$