Investigating Linear Quadratic Systems
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Do all linear quadratic systems have two solutions? 

Do all linear quadratic systems have a solution?

Let's investigate and find the answers to these questions
in connection with quadratics in one variable.

Solve the following linear quadratic systems graphically.

Investigation #1:
Solve this system of equations:

Some linear quadratic systems have two solutions because the straight line crosses the parabola in two locations.

Investigation #2:
Solve this system of equations:

Some linear quadratic systems have one solution because the straight line is tangent to the parabola in only one location.

 

Investigation #3:
Solve this system of equations:

 

Some linear quadratic systems have no solutions because the straight line and the parabola never intersect.

 

Do all linear quadratic systems have two solutions?   No

Do all linear quadratic systems have a solution?  No