Mastering Systems of Equations through Graphing

The video tutorial explains how to solve a system of linear equations by graphing. It begins by ensuring both equations are in slope-intercept form. The first equation, y = -1/3x + 9, is graphed by identifying the slope and y-intercept, plotting points, and drawing the line. The process is repeated for the second equation, y = 2x - 5. The solution is found at the intersection of the two lines, which is the coordinate point (6, 7).

What is the first step when solving a system of linear equations by graphing?

• Plot the x-intercept

• Calculate the determinant

• Ensure both equations are in slope-intercept form

• Identify the intersection point

In the equation y = -1/3x + 9, what is the slope?

• 9

• -9

• -1/3

• 1/3

Where do you plot the y-intercept for the equation y = -1/3x + 9?

• At (0, -1/3)

• At (9, 0)

• At (-1/3, 0)

• At (0, 9)

How do you use the slope -1/3 to plot additional points for the line y = -1/3x + 9?

• Up 1, left 3

• Down 1, right 3

• Up 3, right 1

• Down 3, left 1

What is the y-intercept of the equation y = 2x - 5?

• 5

• 2

• -2

• -5

How can you express the slope of 2 in the equation y = 2x - 5?

• -1/2

• 2/1

• 1/2

• -2/1

Where do you plot the y-intercept for the equation y = 2x - 5?

• At (0, -5)

• At (-5, 0)

• At (2, 0)

• At (0, 2)

How do you use the slope 2 to plot additional points for the line y = 2x - 5?

• Up 1, right 2

• Up 2, right 1

• Down 1, right 2

• Down 2, right 1

What is the solution to the system of equations y = -1/3x + 9 and y = 2x - 5?

• (-6, -7)

• (7, 6)

• (6, 7)

• (-7, -6)

What does the intersection point of the two lines represent?

• The midpoint of the two lines

• The solution to the system of equations

• The x-intercept of the second line

• The y-intercept of the first line