SOLUTION: dear tutors, plz help me find the value of a and b so that x/a + y/b =1 passes through (3,-2) and (9,2). I've already tried answering it but i dont know how.. i solved the value

Algebra ->  College  -> Linear Algebra -> SOLUTION: dear tutors, plz help me find the value of a and b so that x/a + y/b =1 passes through (3,-2) and (9,2). I've already tried answering it but i dont know how.. i solved the value      Log On


   

Question 48025: dear tutors, plz help me find the value of a and b so that x/a + y/b =1 passes through (3,-2) and (9,2).
I've already tried answering it but i dont know how..
i solved the value of x and y..
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+%28x%2Fa%29+%2B+%28y%2Fb%29+=+1+

(3,-2) --> +%283%2Fa%29+%2B+%28%28-2%29%2Fb%29+=+1+
--> now multiply all terms by ab
+%283%2Fa%29%28ab%29+%2B+%28%28-2%29%2Fb%29%28ab%29+=+%28ab%29+
+3b+-+2a+=+ab+

(9,2) --> +%289%2Fa%29+%2B+%282%2Fb%29+=+1+
--> now multiply all terms by ab, again
+%289%2Fa%29%28ab%29+%2B+%282%2Fb%29%28ab%29+=+%28ab%29+
+9b+%2B+2a+=+ab+

Now we have
3b - 2a = ab and
9b + 2a = ab

Lets add them:
12b = 2ab
2a = 12
--> a = 6

Now, +9b+%2B+2a+=+ab+ gives 9b + 12 = 6b
3b = -12
b = -4

So we have +%28x%2F6%29+%2B+%28y%2F%28-4%29%29+=+1+
+%28x%2F6%29+-+%28y%2F4%29+=+1+

CHECK: use (3,-2):
+%283%2F6%29+-+%28%28-2%29%2F4%29+
+%281%2F2%29+%2B+%281%2F2%29+
is 1... correct

CHECK: use (9,2)
+%289%2F6%29+-+%282%2F4%29+
+%283%2F2%29+-+%281%2F2%29+
is 1... correct

jon