Question

Which systems of equations have exactly one solution?

Choose all answers that are correct.
1. y = 2x
y=2x+1

2 . x =5
y = -4

3. y = x+6
y -6 =x

4 . y= 3x+ 4
y =3

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=-(1)/(3) \\ \\ (x,y)=(-(1)/(3),3) - one \ solution`

The answer is 2 and 4.