Understanding Solutions to Systems of Equations

The video tutorial explains how to determine if ordered pairs are solutions to a system of equations. It demonstrates the process by substituting the pairs (9, -2) and (3, 2) into two equations. The pair (9, -2) satisfies both equations, making it a solution, while (3, 2) does not satisfy the second equation, thus not a solution. The tutorial emphasizes the need for a pair to satisfy all equations in the system to be considered a solution.

What must an ordered pair do to be considered a solution to a system of equations?

• Satisfy at least one equation

• Satisfy the equation with the smallest degree

• Satisfy both equations

• Satisfy the equation with the highest degree

What is the result of substituting x = 9 and y = -2 into the equation y = -2/3x + 4?

• -2 = -10 + 4

• -2 = -4 + 4

• -2 = -8 + 4

• -2 = -6 + 4

After simplifying, what does the equation -2 = -6 + 4 become?

• -2 = 0

• -2 = -4

• -2 = -2

• -2 = 2

What is the result of substituting x = 9 and y = -2 into the equation x + 4y = 1?

• 9 + (-8) = 1

• 9 - (-8) = 1

• 9 - 8 = 1

• 9 + 8 = 1

What conclusion can be drawn if an ordered pair satisfies both equations in a system?

• It is a solution to the system

• It is not a solution to the system

• It is a solution to only one equation

• It is a solution to neither equation

What is the result of substituting x = 3 and y = 2 into the equation y = -2/3x + 4?

• 2 = -4 + 4

• 2 = 2 + 4

• 2 = -2 + 4

• 2 = 0 + 4

What does the equation 2 = -2 + 4 simplify to?

• 2 = -2

• 2 = 4

• 2 = 2

• 2 = 0

What is the result of substituting x = 3 and y = 2 into the equation x + 4y = 1?

• 3 + 8 = 1

• 3 + 8 = 0

• 3 + 8 = 3

• 3 + 8 = 11

What conclusion can be drawn if an ordered pair does not satisfy both equations in a system?

• It is a solution to the system

• It is a solution to neither equation

• It is not a solution to the system

• It is a solution to only one equation

What is the final conclusion about the ordered pair (3, 2) regarding the system of equations?

• It satisfies both equations

• It satisfies only the first equation

• It satisfies only the second equation

• It satisfies neither equation