What is the point of intersection of 3x - 2y - 8 = 0 and 2x - y = 16

Expert Answers
justaguide eNotes educator| Certified Educator

The point of intersection of the lines 3x - 2y - 8 = 0 and 2x - y = 16 has to be determined.

2x - y = 16

=> y = 2x - 16

Substitute in 3x - 2y - 8 = 0

=> 3x - 2*(2x - 16) - 8 = 0

=> 3x - 4x + 32 - 8 = 0

=> -x + 24 = 0

=> x = 24

y = 32

The point of intersection of the lines 3x - 2y - 8 = 0 and 2x - y = 16 is (24, 32)

givingiswinning | Student

y = 2x - 16

plug it into 3x - 2y - 8 = 0 as y

3x - 2 ( 2x - 16) - 8 = 0 

simplify

3x - 4x + 32 - 8

-x + 24

-x = -24

x = 24

plug in 24 as x

3(24) - 2y - 8 = 0

72 - 2y - 8

64 - 2y = 0

-2y = -64

y = 32

(24 , 32) 

atyourservice | Student

3x - 2y - 8 = 0 and 2x - y = 16

y = 2x - 16

plug it into 3x - 2y - 8 = 0 as y

3x - 2 ( 2x - 16) - 8 = 0 

simplify:

3x - 4x + 32 - 8

-x + 24

-x = -24

x = 24

now plug in 24 as x

3(24) - 2y - 8 = 0

72 - 2y - 8

64 - 2y = 0

-2y = -64

y = 32

(24 , 32) is the point