Question

entering numerical answers
this question asks for a number answer. acceptable answers include whole numbers, integers (negative numbers), and decimal values. (these questions will normally require you to do calculations by hand or with a computer before you enter a final answer.)
if a question has no solution, click the yellow up arrow to choose dne-- or likewise to enter $\infty$ or $\pi$.
if a system of equations has no solution, select the option for
o solution\. if it has infinitely many solutions, select \infinite number of solutions\. if those options are not available, click the yellow up arrow to choose dne or $\infty$, respectively. (in rare cases that the yellow arrow isnt available, you may need to enter dne for \does not exist\, oo for infinity, or -oo for negative infinity.)
if your answer is not an exact value, youll want to enter at least 3 decimal places unless the problem specifies otherwise.
try it out:
enter the number 32.6669 below exactly (no rounding).
32.6669
enter the number 32.6669 rounded to the nearest hundredth (two decimal places).
32.67
enter the result of $32.6669 \div 0$
enter the solution to this system of equations which has infinitely many solutions.
$\

$$\begin{cases} x = 2y \\\\ y = x - y \\end{cases}$$

$
one solution:

Explanation:

Step1: Evaluate division by zero

Division by zero is undefined, so $32.6669 \div 0$ has no valid numerical result.

Step2: Analyze the system of equations

Substitute $x=2y$ into $y=x-y$:
$y = 2y - y$
$y = y$
This is an identity, true for all $y$, so there are infinitely many solutions parameterized by $y$: $x=2y$, where $y$ is any real number.

Answer:

1. $\infty$ (or DNE, as division by zero is undefined)
2. Infinite number of solutions, where $x=2y$ for any real number $y$