Answered

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 :

naǫ
1.
[tex]y=2x \\ y=2x+1 \\ \\ 2x=2x+1 \\ 2x-2x=1 \\ 0=1 \\ not \ true - no \ solution[/tex]

2.
[tex]x=5 \\ y=-4 \\ already \ solved - one \ solution[/tex]

3.
[tex]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[/tex]

4.
[tex]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[/tex]

The answer is 2 and 4.

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