Question

1.)Y=5x-9

Y=5x+9

2.)y=6x+2
Y=3x+1
3.)y=8x-2
Y-8x=-2
Determine whether the system of linear equation has one solution,infinitely many solution,or no solution.

Answer 1

1) no solution

`y=5x-9 \\ y=5x+9 \\ \\ 5x-9=5x+9 \\ 5x-5x=9+9 \\ 0=18 \\ \hbox{false}`

2) one solution

`y=6x+2 \\ y=3x+1 \\ \\ 6x+2=3x+1 \\ 6x-3x=1-2 \\ 3x=-1 \\ x=-(1)/(3) \\ \\ y=3 * (-(1)/(3))+1=-1+1=0 \\ \\ (-(1)/(3),0)`

3) infinitely many solutions

`y=8x-2 \\ y-8x=-2 \\ \Downarrow \\ y=8x-2 \\ y=8x-2 \\ \\ 8x-2=8x-2 \\ 8x-8x=-2+2 \\ 0=0 \\ \hbox{true}`