Solving Systems of Equations

The video tutorial guides students through solving systems of equations visually by graphing. It begins with an introduction to the exercise, followed by detailed steps to graph two linear equations. The tutorial explains how to identify the y-intercept and slope, plot the equations, and find their intersection point. Finally, it verifies the solution by substituting the intersection point into both equations.

What is the purpose of the exercise introduced in the video?

• To memorize equations

• To practice solving systems of equations visually

• To learn how to graph linear equations

• To understand the concept of slope

What are the two equations given in the video?

• y = 7/5x - 5 and y = 3/5x - 1

• y = 5x - 7 and y = 2x + 4

• y = x - 2 and y = 4x + 3

• y = 2x + 3 and y = -x + 1

What is the y-intercept of the first equation?

• -5

• 0

• 5

• 7

What is the slope of the first equation?

• 7/5

• 3/5

• 5/7

• 1/5

How many units up does the line move for every 5 units to the right in the first equation?

• 2 units

• 3 units

• 5 units

• 7 units

What is the y-intercept of the second equation?

• -1

• 0

• 1

• 3

What is the slope of the second equation?

• 3/5

• 5/3

• 7/5

• 1/3

At what point do the two lines intersect?

• (5, 2)

• (2, 5)

• (1, 1)

• (0, 0)

How can you verify the intersection point is correct?

• By checking if it lies on the x-axis

• By substituting the point into both equations

• By measuring the distance between the lines

• By drawing a perpendicular line

What is the result of substituting the intersection point into both equations?

• It results in a contradiction

• It satisfies neither equation

• It satisfies only one equation

• It satisfies both equations