Answer:
One possible ordered pair is (0,-1)
Another ordered pair is (1/6, 0)
There are infinitely many ordered pairs
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Explanation:
If x = 0, then y is...
6x-y = 1
6(0)-y = 1
0-y = 1
-y = 1
y = -1
So one ordered pair solution is (x,y) = (0,-1). This is the y intercept which always occurs when x = 0.
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If y = 0, then,
6x-y = 1
6x-0 = 1
6x = 1
x = 1/6
meaning that (x,y) = (1/6, 0) is another ordered pair solution. This is the x intercept which always occurs when y = 0.
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As you can see, we can plug in any number we want for x or y (pick one only). Whatever you pick, you solve for the other unknown variable. Since we can pick infinitely many values to plug in, this means there are infinitely many ordered pair solutions. Visually, there are infinitely many points that are along the line 6x-y = 1
Note: 6x-y = 1 solves to y = 6x-1. It has slope 6 and y intercept 1.
