Understanding Solutions to Linear Equations

The video tutorial explains how to solve a linear equation by completing ordered pairs. It demonstrates substituting known values for X or Y to find the corresponding unknown value, ensuring the pair satisfies the equation. The tutorial covers three scenarios: solving for Y when X=0, solving for X when Y=0, and solving for Y when X=-1. It concludes with a graphical verification of the solutions by plotting the points on a graph to confirm they lie on the line represented by the equation.

What is the first step in determining if an ordered pair is a solution to a linear equation?

• Graph the equation

• Solve for x

• Substitute the values into the equation

• Solve for y

When x = 0, what is the y-value that makes the ordered pair a solution to the equation -4x + 3y = 7?

• 7/3

• 0

• 3

• 7

What does the ordered pair (0, 7/3) represent on the graph of the equation -4x + 3y = 7?

• x-intercept

• y-intercept

• Origin

• Slope

If y = 0, what is the x-value that makes the ordered pair a solution to the equation -4x + 3y = 7?

• -7/4

• 7/4

• 4

• 0

What does the ordered pair (-7/4, 0) represent on the graph of the equation -4x + 3y = 7?

• Origin

• Slope

• x-intercept

• y-intercept

When x = -1, what is the y-value that makes the ordered pair a solution to the equation -4x + 3y = 7?

• 3

• -1

• 0

• 1

What is the first step in solving the equation 4 + 3y = 7 for y?

• Divide both sides by 3

• Multiply both sides by 3

• Add 4 to both sides

• Subtract 4 from both sides

What is the purpose of graphically verifying the solutions to the equation -4x + 3y = 7?

• To calculate the x-intercept

• To determine the y-intercept

• To check if the points lie on the line

• To find the slope

Which of the following points is NOT a solution to the equation -4x + 3y = 7?

• (-1, 1)

• (-7/4, 0)

• (1, 0)

• (0, 7/3)

What does it mean if a point lies on the graph of the equation -4x + 3y = 7?

• The point is the midpoint

• The point is the origin

• The point is a solution to the equation

• The point is the slope