Understanding Solutions to Linear Equations

The video tutorial explains how to find solutions to the linear equation X - 4Y = 6. It demonstrates the process of substituting values for X or Y to find ordered pairs that satisfy the equation. The tutorial provides four solutions, verifies them graphically, and emphasizes the infinite number of solutions possible for linear equations in two variables.

What is an ordered pair in the context of a linear equation?

• A pair of numbers that do not satisfy the equation

• A pair of numbers that satisfy the equation

• A pair of numbers that are always negative

• A pair of numbers that are always positive

What is the Y value when X is set to 0 in the equation X - 4Y = 6?

• 1.5

• -1.5

• 0

• -6

What ordered pair is obtained when Y is set to 0 in the equation X - 4Y = 6?

• (0, -6)

• (6, 0)

• (-6, 0)

• (0, 6)

What is the X value when X is set to -1 in the equation X - 4Y = 6?

• -1

• 0

• 6

• 1

What is the Y value when X is set to -1 in the equation X - 4Y = 6?

• -7

• 7

• -1.75

• 1.75

What is the result of dividing -7 by 4 in decimal form?

• -1.75

• 1.5

• 1.75

• -1.5

What ordered pair is obtained when Y is set to -2 in the equation X - 4Y = 6?

• (2, 2)

• (-2, 2)

• (2, -2)

• (-2, -2)

How do we verify the solutions to the equation X - 4Y = 6 graphically?

• By checking if the points lie on the line of the equation

• By checking if the points lie on the X-axis

• By checking if the points lie on the Y-axis

• By checking if the points lie on the origin

What does the equation X - 4Y = 6 represent graphically?

• A circle

• A parabola

• A line

• A hyperbola

What is the significance of finding multiple solutions to a linear equation?

• It shows the equation has no solutions

• It shows the equation has a unique solution

• It shows the equation has infinite solutions

• It shows the equation is inconsistent