Consider the two equations, y=5(x-2)^2-6 and (y+2)^2=9
how many solutions are there to this system? without solving, give a convincing argument explain why there are that many solutions to the system.

One solution. A system of linear equations has one solution when the graphs intersect at a point.

1\small{1}

1

2\small{2}

2

3\small{3}

3

-1\small{\llap{-}1}

-

1

1\small{1}

1

2\small{2}

2

3\small{3}

3

-1\small{\llap{-}1}

-

1

yy

y

xx

x

No solution. A system of linear equations has no solution when the graphs are parallel.

1\small{1}

1

2\small{2}

2

3\small{3}

3

-1\small{\llap{-}1}

-

1

1\small{1}

1

2\small{2}

2

3\small{3}

3

-1\small{\llap{-}1}

-

1

yy

y

xx

x

Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.

Step-by-step explanation:

y=x+9

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step-by-step explanation: