3x - 2y = 6
6x - 4y = 12
Show that the simultaneous equations have an infinite number of solutions.
Using an augmented matrix?
Perform some elementary row operations on the augmented matrix to get to reduced row echelon form.
Divide R1 by 3
Multiply R1 by -6 and add to R2
If there is a row in the augmented matrix containing all zeros (to the left and right of the line), then it is as if that row could be completely ignored, as it represents 0 = 0, which by itself is inconclusive. Whether or not there are solutions depends on the remaining row. The remaining row consists of an equation in 2 non-zero variables. We have more variables than we have equations, thus indicating an infinite number of solutions.