Classify the systems of equations based on the number of solutions they have.

1. x + 2y = 1
3x + 6y = 3

2. 2y - x = 12
2y - 2x = 10

3. 2/5y - 8/5x 1
2y - 3x = 5

1 answer

1. This system of equations has infinitely many solutions because the second equation is a multiple of the first equation.

2. This system of equations has no solutions because the slopes of the two equations are equal but the y-intercepts are different.

3. This system of equations has one unique solution because the two equations are not multiples of each other and have different slopes.
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