SOLUTION: Please may you help me solve this;line A is 3x-4y+11=0 and line B is 2x-3y+9=0.The lines are line A,B and C pass through point A.Without finding point A,find the equation of line C

Algebra ->  Radicals -> SOLUTION: Please may you help me solve this;line A is 3x-4y+11=0 and line B is 2x-3y+9=0.The lines are line A,B and C pass through point A.Without finding point A,find the equation of line C      Log On


   

Question 1085743: Please may you help me solve this;line A is 3x-4y+11=0 and line B is 2x-3y+9=0.The lines are line A,B and C pass through point A.Without finding point A,find the equation of line C if its slope is -2/3

Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A:3x-4y%2B11=0
B:2x-3y%2B9=0
.
.
C:y=%28-2%2F3%29x%2Bb
C:3y=-2x%2B3b
C:2x%2B3y-3b=0
Let the point A be (c,d).
1.3c-4d%2B11=0
2.2c-3d%2B9=0
3.2c%2B3d-3b=0
Add 2 and 3,
2c-3d%2B9%2B2c%2B3d-3b=0
4.4c%2B9-3b=0
Multiply 1 by 3 and 2 by -4 and add,
9c-12d%2B33-8c%2B12d-36=0
c-3=0
c=3
Substituting back into 4,
4%283%29%2B9-3b=0
12%2B9-3b=0
3b=21
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.
.
C:2x%2B3y-21=0
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.
.
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Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
we can write line C in point slope form
:
y = -2x/3 +b
:
3y = -2x +3b
:
2x +3y = 3b
:
we have the following three equations
:
1) 3x -4y = -11
2) 2x -3y = -9
3) 2x +3y = 3b
:
add equations 2 and 3
:
4x = 3b -9
x = 3b/4 -9/4
:
substitute for x in equations 1 and 2
:
1) 3(3b/4 -9/4) -4y = -11
9b/4 -27/4 -4y = -11
9b -27 -16y = -44
9b -16y = -17
:
2) 2(3b/4 -9/4) -3y = -9
6b/4 -18/4 -3y = -9
6b -18 -12y = -36
6b -12y = -18
:
we have two equations in two unknowns
:
3) 9b -16y = -17
4) 6b -12y = -18
:
divide both sides of equation 4 by 6
:
b -2y = -3
:
solve for y
:
2y = 3 +b
y = 3/2 +b/2
:
substitute for y in equation 3
:
9b -16(3/2 +b/2) = -17
9b -24 -8b = -17
b = 7
:
***************
y = -2x/3 +7
:
3y = -2x +21
:
2x +3y -21 = 0
***************
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