Determining Solutions for Linear 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 values of the ordered pairs into the equations and checking if they satisfy both equations. The tutorial verifies that the pair (9, -2) is a solution, while (3, 2) is not, emphasizing the need for both equations to be true for a pair to be a solution.

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

• Satisfy at least one equation

• Satisfy both equations

• Satisfy the second equation only

• Satisfy the first equation only

What is the first step in verifying if (9, -2) is a solution to the system?

• Substitute 9 for y and -2 for x

• Substitute -2 for x and 9 for y

• Substitute 9 for x and -2 for y

• Substitute -2 for y and 9 for x

What is the result of simplifying -2 = -2/3 * 9 + 4?

• -2 = -6 + 4

• -2 = -3 + 4

• -2 = -8 + 4

• -2 = -4 + 4

What does the equation -2 = -2/3 * 9 + 4 simplify to?

• -2 = -2

• -2 = -4

• -2 = 0

• -2 = 2

What is the result of substituting (9, -2) into the second equation x + 4y = 1?

• 9 + 4 * -1 = 1

• 9 + 4 * 2 = 1

• 9 + 4 * -2 = 1

• 9 + 4 * 1 = 1

What is the simplified form of 9 + 4 * -2?

• 1

• -1

• 2

• 0

What is the first step in verifying if (3, 2) is a solution to the system?

• Substitute 3 for x and 2 for y

• Substitute 2 for y and 3 for x

• Substitute 3 for y and 2 for x

• Substitute 2 for x and 3 for y

What is the result of simplifying 2 = -2/3 * 3 + 4?

• 2 = -2 + 4

• 2 = -1 + 4

• 2 = -4 + 4

• 2 = -3 + 4

What does the equation 2 = -2/3 * 3 + 4 simplify to?

• 2 = 2

• 2 = 0

• 2 = 4

• 2 = -2

What is the result of substituting (3, 2) into the second equation x + 4y = 1?

• 3 + 4 * 1 = 1

• 3 + 4 * 2 = 1

• 3 + 4 * 0 = 1

• 3 + 4 * -2 = 1