Question

Which systems of equations have exactly one solution?

Answer 1

1.
$y=2x \\ y=2x+1 \\ \\ 2x=2x+1 \\ 2x-2x=1 \\ 0=1 \\ not \ true - no \ solution$

2.
$x=5 \\ y=-4 \\ already \ solved - one \ solution$

3.
$y=x+6 \\ y-6=x \\ \\ y=x+6 \\ y=x+6 \\ \\ x+6=x+6 \\ x-x=6-6 \\ 0=0 \\ true - infinitely \ many \ solutions$

4.
$y=3x+4 \\ y=3 \\ \\ 3=3x+4 \\ 3-4=3x \\ -1=3x \\ x=-\frac{1}{3} \\ \\ (x,y)=(-\frac{1}{3},3) - one \ solution$

The answer is 2 and 4.