By using the parallel condition and the fact that the distance to the origin is the same, we will see that a = 1 and b = 2.
First, remember that two lines are parallel if have the same slope and different y-intercept.
In this case, we know that
y = a*x - 1
b*y - (a + 1)*x = 2
Are parallel, if we write both of them in the slope-intercept form, we get:
y = a*x - 1
y = (a + 1)*x/b + 2/b
Note that because both of the lines are parallel, the slopes must be equal, then we have that:
(a + 1)/b = a
Then if we know that the distance of both lines to the origin is the same, we have that:
|-1/(√(a^2 + 1))| = | (2/b)/(√(((a + 1)/b)^2 + 1))|
Because the slopes are equal the denominators are equal, this means that:
|-1| = |2/b|
And the y-intercepts must be different, this means that:
b = 2
now we can solve:
(a + 1)/b = a
(a + 1)/2 = a
a + 1 = 2a
1 = 2a - a = a
a = 1 and b = 2.
If you want to learn more about linear equations, you can read:
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