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?


Standard options: 
A. Solve linear equations in one variable.
B. Analyze and solve pairs of simultaneous linear equations.


Your response:
Thought: The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001392

8
options: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
problem_activity: Problem 1
In equations (a)–(d) below, the solution,
$$x$$
, to the equation depends on the constant,
$$a$$
. Assuming
$$a$$
is positive, what is the effect of increasing
$$a$$
on the solution? Does it increase, decrease, or remain unchanged?
Give a reason for your answer that can be understood without solving the equation.
a.
$$x-a=0$$
b.
$$ax=1$$
c.
$$ax=a$$
d.
$$\frac{x}{a}=1$$
Problem 2
Which of the following equations have the same solution(s)? Give reasons for your answer that do not depend on solving the equations.
a.
$${x+3=5x-4}$$
b.
$${x-3=5x+4}$$
c.
$${2x+8=5x-3}$$
d.
$${10x+6=2x-8}$$
e.
$${10x-8=2x+6}$$


correct_option_index: 1