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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Where C is a real number, the lines 3 x + 2 y = C , 2 x + y = 5 , and x - y = 4 are concurrent. Determine the value of C .

To determine

To find:

The value of C, Where C is a real number, given that the lines 3x+2y=C, 2x+y=5, and x-y=4 are concurrent.

Explanation

If the lines are concurrent, they will intersect at the same point.

Initially solve for x and y from any two equation and then substitute that point in the third equation.

Let the first two equations be 3x+2y=C, and 2x+y=5.

Find y from the equation 3x+2y=C,

2y=C-3x

Divide both sides by 2,

y=C-3x2

Substitute y=C-3x2 in 2x+y=5,

2x+C-3x2=5

Multiply both sides by 2,

4x+C-3x=10

x=10-C

Substitute x=10-C in y=C-3x2,

y=C-310-C

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