Find the point of intersection of 4x - 3y - 7 = 0 2x + 3y + 8 = 0 8x + 3y + 9 = 0

Question

The three lines are concurrent and the answer is supposed to be (-1/6,-23/9).

Answer 1

4x-3y-7=0

2x+3y-8=0

8x+3y-9=0

Is there a typo ??

I'm going to assume that in the first equation, -7 should be +7. If I'm wrong, let me know.

 

4x-3y+7=0

2x+3y-8=0

4x-3y=-7

2x+3y=8

add

6x=1

x=1/6

find y from equation one

4(1/6)-3y+7=0

(4/6)-3y+7=0

(4/6)+7=3y

7 2/3=3y

23/3=3y

y=23/9

x=1/6 and y=23/9, (1/6,23/9)  (answer)

checking equation 3...

8(1/6)+3(23/9)=9

8/6 + 23/3=9

8/6 + 46/6=9

54/6=99=9

checking equation 2...

2(1/6)+3(23/9)=8

1/3 + 23/3=8

24/3=8

8=8

checking equation 1 again...

4(1/6) -3(23/9)=-7

2/3-23/3=-7

-21/3=-7

-7=-7

Everything seems to work. Check the problem again.

 

Answer 2

This system of has no solution.

Answer 3

Solve for one pair:

4x - 3y - 7 = 0

2x + 3y - 8 = 0

 

6x - 15 = 0

6x = 15

x = 15/6

x = 5/2

 

This does not match the "supposed" solution.