Solving Equations Using Graphs: Simultaneous Equations and Inequalities on a Graph

The video tutorial explains how to solve simultaneous equations by finding the intersection of lines on a graph. It also covers shading regions defined by inequalities, plotting lines, testing coordinates, and identifying the correct region on the graph. The tutorial concludes with a summary of the process and marks allocation.

What is the solution to the simultaneous equations 3y = 2x + 6 and 4x + 3y = 24?

• x = 3, y = 4

• x = 4, y = 3

• x = 2, y = 5

• x = 5, y = 2

Which of the following inequalities is NOT part of the problem?

• 3y is less than or equal to 2x plus 6

• x plus y is greater than or equal to 4

• y is less than or equal to 0

• x is greater than or equal to 0

What is the first step in shading the region defined by the inequalities?

• Erase all existing lines

• Draw random lines

• Shade the entire graph

• Identify lines already drawn on the grid

How do you determine the line for the inequality x + y = 4?

• By guessing the coordinates

• By finding two points that add up to 4

• By drawing a vertical line

• By drawing a horizontal line

Which coordinate pair is used to test the inequality 3y ≤ 2x + 6?

• (1, 1)

• (0, 0)

• (10, 10)

• (5, 5)

What is the result of testing the coordinate (10, 3) for the inequality 4x + 3y ≤ 24?

• False, the inequality does not hold

• The coordinate is not on the graph

• True, the inequality holds

• Cannot be determined

What is the final step in identifying the region of interest?

• Draw a new line

• Erase all other regions

• Shade the entire graph

• Label the region as R

Why is it important to read the inequality symbols correctly?

• To draw more lines

• To change the coordinates

• To erase the graph

• To ensure the correct side of the line is shaded

What is the purpose of using multiple coordinates when testing inequalities?

• To draw more lines

• To verify the correct region is shaded

• To erase incorrect lines

• To confuse the solver

How many marks are available for correctly identifying the region of R?

• Three marks

• Two marks

• Four marks

• One mark