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MA_775_DIABLO [31]
2 years ago
11

the line y=ax-1 is parallel to the line by-(a+1)x=2. These two lines have the same distance to the origin. find a and b

Mathematics
1 answer:
Levart [38]2 years ago
6 0

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.

<h3>How to find the values of a and b?</h3>

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:

brainly.com/question/1884491

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Answer:

Pencils = 325 ; Pens = 975 ; Markers = 650

Step-by-step explanation:

Let :

Number of Pencils = x

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z = 2x

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Write z and y in terms of x in the equation :

x + 3x + 2x = 1950

6x = 1950

Divide both sides by 6

6x / 6 = 1950 / 6

x = 325

Number of pencils = 325

Pens = 3 * 325 = 975

Markers = 2 * 325 = 650

Pencils = 325 ; Pens = 975 ; Markers = 650

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Step-by-step explanation: 800/x=100/17

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