A graph of two intersecting inequalities on a coordinate plane, origin O. Each axis from negative 10 to 5, by 2’s. The first dashed line starts below x axis and right of y axis, goes through negative 8 comma negative 8, 0 comma 0, and 8 comma 8. The region above the dashed line is shaded. Second line starts on negative 8 comma 10, goes through negative 4 comma 2, and ends on 2 comma negative 10. The region above the dashed line is shaded.
7.2
Activity
Each riddle consists of two conditions. For each riddle,
Find a pair of numbers that satisfy the first condition.
Find a pair of numbers that satisfy the second condition.
Find a pair of numbers that satisfy both conditions.
Decide whether there could be more than one solution.
Write a system of equations or inequalities that represent the riddle.
I’m thinking of two numbers. One is more than twice the other. Their sum is less than 30.
I’m thinking of two numbers. Their sum is more than 15. Their difference is more than 1.
I’m thinking of two numbers. Their sum is 15. Their difference is 1.
Think of your own riddles about a pair of numbers.
Make a riddle with multiple pairs of numbers that will work.
Make a riddle with only one pair of numbers that will work.
7.3
Activity
For each question:
Draw a graph that represents the equation or equations.
Figure out how many regions the lines split the plane into.
Play a game with your partner.
Partner A: Think of one of the regions.
Partner B: Without pointing to the coordinate plane, use the lines to ask questions of your partner about the region they have chosen. When you think you know which region they are thinking of, point to the region and ask your partner if you are correct. If you are correct, shade the entire region.