Intersection and Properties of Functions

The video tutorial explains how to solve a system of equations using the substitution method. It begins by substituting y in the second equation and solving for x, leading to a quadratic equation. The quadratic is solved by factoring, yielding two solutions. These solutions are verified by finding corresponding y-values and graphically checking the points of intersection on a coordinate plane.

What is the first step in using the substitution method for solving a system of equations?

• Graphing the equations

• Eliminating one variable

• Substituting one equation into the other

• Solving for x in both equations

After substituting y = x - 2 into the second equation, what form does the equation take?

• x - 2y = 3

• x + y = 3

• x^2 - 2x = 3

• x^2 + 2x = 3

What is the next step after obtaining the quadratic equation x^2 - 2x - 3 = 0?

• Use the quadratic formula

• Set the equation equal to zero and factor

• Solve by completing the square

• Graph the equation

What are the x-values obtained after solving the quadratic equation x^2 - 2x - 3 = 0?

• x = 2 and x = -3

• x = 3 and x = -1

• x = 0 and x = 3

• x = 1 and x = -2

How do you find the corresponding y-value for x = -1 using the equation y = x - 2?

• Substitute x = -1 into y = 3x

• Substitute x = -1 into y = x + 2

• Substitute x = -1 into y = x - 2

• Substitute x = -1 into y = 2x

What is the ordered pair solution when x = 3?

• (3, 1)

• (3, 0)

• (3, 2)

• (3, -1)

What is the purpose of graphing the equations in the final step?

• To check for parallel lines

• To determine the y-intercept

• To verify the solutions by finding points of intersection

• To find the slope of the lines

Which graph represents the equation y = x - 2?

• A horizontal line

• A vertical line

• A diagonal line with a positive slope

• A diagonal line with a negative slope

What type of function is represented by the equation y = 3/x?

• Quadratic function

• Linear function

• Rational function

• Exponential function

How many points of intersection are there between the graphs of y = x - 2 and y = 3/x?

• Two

• One

• Three

• None