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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 :

naǫ
1) no solution
[tex]y=5x-9 \\ y=5x+9 \\ \\ 5x-9=5x+9 \\ 5x-5x=9+9 \\ 0=18 \\ \hbox{false}[/tex]

2) one solution
[tex]y=6x+2 \\ y=3x+1 \\ \\ 6x+2=3x+1 \\ 6x-3x=1-2 \\ 3x=-1 \\ x=-\frac{1}{3} \\ \\ y=3 \times (-\frac{1}{3})+1=-1+1=0 \\ \\ (-\frac{1}{3},0)[/tex]

3) infinitely many solutions
[tex]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}[/tex]

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