   Chapter 10.5, Problem 49E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Where a and b are real numbers, a + b ,   a - 2 b is the point of intersection for the lines 3 x - 2 y = 19 , and 2 x - 5 y = 9 . Find the values of a and b .

To determine

To find:

The value of a and b, Where a and b are real numbers, given that a+b, a-2b is the point of intersection for the lines 3x-2y=19, and 2x-5y=9.

Explanation

Find the point of intersection of the two lines 3x-2y=19, and 2x-5y=9.

Find y from the equation 3x-2y=19,

2y=3x-19

Divide both sides by 2,

y=3x-192

Substitute y=3x-192 in 2x-5y=9,

2x-53x-192=9

2x-15x-952=9

Multiply both sides by 2,

4x-15x+95=18

-11x=18-95

-11x=-77

x=-77-11

x=7

Substitute x=7 in y=3x-192,

y=37-192,

y=21-192,

y=22

y=1

Thus the point of intersection is 7, 1

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