few_shots: 
Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Concept/skill: 
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Answer: 
No. Completing neither of these problems requires replacing one equation by the sum of that equation and a multiple of the other equation.

Now, does the following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001392_neg_0

8
standard_description: Solve problems involving velocity and other quantities that can be represented by vectors.
problem_activity: Task
Decide which value is closest to the answer for each of the following questions. Explain your reasoning.
8 bottles each contained 1.2 liters of water. About how many liters of water were there all together?
| 0.1 | 1 | 10 | 100 |
|-----|---|----|-----|
A school bought 8.5 kilograms of apples. If apples cost $2.45 per kilogram, about how much did they pay (in dollars)?
| 0.2 | 2 | 20 | 200 |
|-----|---|----|-----|
A laptop contains about 0.0006 kilograms of gold. If a manufacturer plans to produce 10,100 of these laptops, about how many kilograms of gold are needed?
| 0.6 | 6 | 60 | 600 |
|-----|---|----|-----|


aligns: no