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

2 Answers
Mar 24, 2015

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

Mar 24, 2015

#x+2y=2# and #2x+4y=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=-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:

#"All " (x,y) " with " x+2y=2#

#"All " (x, 1-1/2x)#

#"All " (-2y+2, x)#