The "system" of equations can't be solved for (x, y), because there's no "system" of equations given. There's really only one equation.
Either of these two equations can be massaged to look exactly like the other one. And if you graph both equations, you find that they're both the same line on the graph.
ANY point on the line is a solution to both equations ... and we all know how many different points there are on a line.
A irrational number is a number that can't be expressed as a ratio of two whole numbers. That's it.
For examples (in increasing order of difficulty)
1 is a rational number because it is 1/1
0.75 is a rational number because it is equal to 3/4
2.333... (infinite number of digits, all equal to three) is rational because it is equal to 7/3.
sqrt(2) is not a rational number. This is not completely trivial to show but there are some relatively simple proofs of this fact. It's been known since the greek.
pi is irrational. This is much more complicated and is a result from 19th century.
As you see, there is absolutely no mention of the digits in the definition or in the proofs I presented.
Now the result that you probably hear about and wanted to remember (slightly incorrectly) is that a number is rational if and only if its decimal expansion is eventually periodic. What does it mean ?
Take, 5/700 and write it in decimal expansion. It is 0.0057142857142857.. As you can see the pattern "571428" is repeating in the the digits. That's what it means to have an eventually periodic decimal expansion. The length of the pattern can be anything, but as long as there is a repeating pattern, the number is rational and vice versa.
As a consequence, sqrt(2) does not have a periodic decimal expansion. So it has an infinite number of digits but moreover, the digits do not form any easy repeating pattern.
Im not sure but u can search up the name and see online i would help if i could i hope the advise i gave helps just seach up if no one can help im so sorry i wanted to help but idk this stuff yet sorry
Answer:
The least possible quotient is 125.
Step-by-step explanation:
To do this we need to find the greatest 2 digit factor of 10,000.
10,000 = 2*2*2*2*5*5*5*5
So the greatest 2 digit number which will divide exactly into 10,000 is
= 2*2*2*2*5
= 80.
This will give the smallest quotient: 10,000 / 80 = 125.
