SOLUTION: find the equation of the line that passes through the intersection of the given pair of line and satisfies the other given condition. x-y-4=0, 2x+y-5=0; passes through the origi

Algebra ->  Points-lines-and-rays -> SOLUTION: find the equation of the line that passes through the intersection of the given pair of line and satisfies the other given condition. x-y-4=0, 2x+y-5=0; passes through the origi      Log On


   

Question 905827: find the equation of the line that passes through the intersection of the given pair of line and satisfies the other given condition.
x-y-4=0, 2x+y-5=0; passes through the origin
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x+-+y+-+4+=+0+
+2x+%2B+y+-+5+=+0+
------------------
Add the equations
+3x+-+9+=+0+
+3x+=+9+
+x+=+3+
and
+x+-+y+-+4+=+0+
+3+-+y+-+4+=+0+
+y+=+3+-+4+
+y+=+-1+
-----------------
The line you need goes through
( 3, -1 )
( 0, 0 )
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Use the general point-slope formula
+%28+y+-+%28-1%29+%29+%2F+%28+x+-+3+%29+=+%28+0+-+%28-1%29+%29+%2F+%28+0+-+3+%29+
+%28+y+%2B+1+%29+%2F+%28+x+-+3+%29+=+1+%2F+%28-3%29+
+-3%2A%28+y+%2B+1+%29+=+x+-+3+
+-3y+-+3+=+x+-+3+
+x+%2B+3y+=+0+
------------------
check:
Does line pass through origin?
+0+%2B+3%2A0+=+0+
OK
Does line pass through ( 3, -1 ) ?
+3+%2B+3%2A%28-1%29++=+0+
+3+-+3+=+0+
OK