Linear and Quadratic Systems Solutions

The video tutorial explores systems of equations involving linear and quadratic functions. It demonstrates how to determine the number of solution points by examining the intersection points on graphs. Three systems are analyzed: the first and second systems have two solutions each, while the third system has no solutions due to non-intersecting graphs. The tutorial emphasizes that systems with one linear and one quadratic equation can have zero, one, or two solutions, depending on their intersection points.

What types of functions are involved in the systems of equations discussed in the video?

• Linear and exponential

• Quadratic and cubic

• Linear and quadratic

• Exponential and logarithmic

How many solution points are there in the first system discussed?

• One

• None

• Two

• Three

What are the coordinates of the first solution point in the first system?

• (2, 2)

• (0.6, 0.8)

• (1, 0)

• (1.75, 1.5)

In the second system, what is the coordinate of the second solution point?

• (2, 2)

• (1.75, 1.5)

• (0.6, 0.8)

• (1, 0)

What is the coordinate of the first solution point in the second system?

• (1, 0)

• (0.6, 0.8)

• (2, 2)

• (1.75, 1.5)

What is the reason for having no solutions in the third system?

• The graphs intersect at two points

• The graphs do not intersect

• The graphs are parallel

• The graphs intersect at one point

What is a possible outcome when a linear and a quadratic equation are graphed together?

• Always one solution

• Always two solutions

• Zero, one, or two solutions

• Always no solutions

What must you look for to determine the number of solutions in a system of equations?

• The y-intercept of the linear equation

• The slope of the linear equation

• The vertex of the quadratic equation

• The intersection points of the graphs

Which of the following is not a possible number of solutions for a system with one linear and one quadratic equation?

• Zero

• One

• Three

• Two