A linear system may have a unique solution, no solution, or infinitely many solutions. Indicate the type of the system for th following examples by U , N , or I , respectively.

Question

1. 2x+3y=5 4x+6y=10
2. 2x+3y=5 2x+4y=6
3. 2x+3y=5 2x+3y=6

Answer 1

1. One equation is twice the other, but represents the same line. There are an infinite number of (x,y) combinations that satisfy it.

2. Those lines intercept at a point, for one solution.

3. Both equations cannot be true. Those are the equations of parallel lines