Verifying Solutions of Linear Equations

In this lesson, students learn to verify if given coordinate pairs are solutions to the linear equation x - 9y = 12. The process involves substituting x and y values from the pairs into the equation and checking if the result equals 12. The video demonstrates this with four points: (12, 0), (0, 12), (3, -1), and (0, -4/3). Points (12, 0), (3, -1), and (0, -4/3) are confirmed as solutions, while (0, 12) is not. The lesson concludes with graphing the equation to visually confirm the solutions.

What is the equation given in the activity?

• x + 9y = 12

• x + 9y = 0

• x - 9y = 12

• x - 9y = 0

How do you determine if a point is a solution to the equation?

• By ensuring both coordinates are even numbers

• By replacing x and y in the equation and checking if it equals 12

• By graphing the point and checking its distance from the origin

• By checking if the x-coordinate is positive

Why is the point (12, 0) a solution to the equation?

• Because 12 - 9*0 equals 12

• Because 12 + 9*0 equals 12

• Because 12 - 9*0 equals 0

• Because 12 + 9*0 equals 0

Why is the point (0, 12) not a solution to the equation?

• Because 0 + 9*12 equals -108

• Because 0 - 9*12 equals -108

• Because 0 + 9*12 equals 12

• Because 0 - 9*12 equals 12

What operation is used to verify the point (3, -1) as a solution?

• Division

• Multiplication

• Inverse operation of subtraction

• Inverse operation of addition

What is the result of 3 minus a negative 9?

• 12

• -6

• 0

• 3

How is the point (0, -4/3) verified as a solution?

• By checking if 0 + 9*(-4/3) equals 0

• By checking if 0 - 9*(-4/3) equals 12

• By checking if 0 + 9*(-4/3) equals 12

• By checking if 0 - 9*(-4/3) equals 0

Which of the following points is not a solution to the equation?

• (0, 12)

• (12, 0)

• (3, -1)

• (0, -4/3)

What is the additive inverse of -9?

• 9

• -9

• 0

• 18

What is the final result when you replace x and y in the equation with the coordinates of a solution?

• 0

• 9

• 12

• -12