Understanding Ordered Pairs and Solutions in Systems of Equations

The video tutorial explains how to determine if an ordered pair is a solution to a system of equations. It demonstrates the process by substituting the values of X and Y into the equations and checking if the equations hold true. The tutorial also covers transforming equations into the slope-intercept form and solving them to verify solutions.

What is the first step in determining if an ordered pair is a solution to a system of equations?

• Graph the equations.

• Check if the pair is in the correct format.

• Substitute the values into the equations.

• Solve the equations separately.

In the context of ordered pairs, what does the first number represent?

• The Y-coordinate

• The slope

• The X-coordinate

• The constant term

What is the result when substituting the ordered pair (1, 4) into the first equation?

• 1 equals 4

• 4 equals 4

• 4 equals 5

• 1 equals 5

Why is the ordered pair (1, 4) not a solution to the system of equations?

• It satisfies both equations.

• It does not satisfy either equation.

• It only satisfies the first equation.

• It only satisfies the second equation.

What is the purpose of transforming an equation into the slope-intercept form?

• To make it easier to graph.

• To eliminate the Y variable.

• To find the X-intercept.

• To solve for the constant term.

What operation is used to isolate Y in the equation -2X + Y?

• Multiply by 2

• Divide by 2

• Add 2X

• Subtract 2X

What is the result of substituting the ordered pair (1, -1) into the first transformed equation?

• -1 equals 0

• 1 equals -1

• -1 equals -1

• 1 equals 0

What is the result of substituting the ordered pair (1, -1) into the second transformed equation?

• -1 equals 1

• 1 equals -1

• -1 equals -2

• -1 equals -1

Why is the ordered pair (1, -1) considered a solution to the system of equations?

• It satisfies only the first equation.

• It satisfies only the second equation.

• It satisfies both equations.

• It does not satisfy either equation.

What is the significance of verifying solutions in a system of equations?

• To graph the equations accurately.

• To find the slope of the line.

• To determine the Y-intercept.

• To ensure the ordered pair satisfies both equations.