Regents Exam: Algebra I August 2016 (Problem 2 of 37)

The video tutorial explains how to determine the correct solution to an equation with two variables, X and Y, by evaluating four given options. It begins with an introduction to equations and their solutions, followed by a detailed analysis of each option. The tutorial concludes that option 3, which states that the solution is the set of all ordered pairs (X, Y) that make the equation true, is the correct answer. The video emphasizes understanding the graphical representation of equations and the importance of identifying all solutions, not just specific intercepts.

What is the primary goal when determining if two expressions in an equation are equal?

• To calculate the slope of the curve

• To identify the Y intercepts

• To find the X intercepts

• To ensure the left and right sides are equal

What does the first option suggest about the solutions of the equation?

• All Y values that make X zero

• All X values that make Y zero

• All ordered pairs that make the equation true

• All points where the graph crosses the Y axis

Why is the second option not a complete solution to the equation?

• It only considers the X intercepts

• It only considers the Y intercepts

• It includes all ordered pairs

• It focuses on the slope of the curve

Which option correctly defines the solution to an equation with two variables?

• The set of all X values that make Y zero

• The set of all Y values that make X zero

• The set of all ordered pairs that make the equation true

• The set of points where the graph crosses the Y axis

What does the fourth option incorrectly suggest about the solutions of the equation?

• That solutions are based on the slope

• That solutions include all ordered pairs

• That solutions are only the Y intercepts

• That solutions are only the X intercepts