SOLUTION: Find the values of x satisfying the given conditions. y1 = 2x/x-8, y2 = 3/x+7, y1 + y2 = 1

Algebra ->  Expressions -> SOLUTION: Find the values of x satisfying the given conditions. y1 = 2x/x-8, y2 = 3/x+7, y1 + y2 = 1       Log On


   

Question 990921: Find the values of x satisfying the given conditions.
y1 = 2x/x-8, y2 = 3/x+7, y1 + y2 = 1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y%5B1%5D+=+2x%2F%28x-8%29, y%5B2%5D+=+3%2F%28x%2B7%29,
given condition: y%5B1%5D+%2B+y%5B2%5D+=+1

2x%2F%28x-8%29%2B3%2F%28x%2B7%29=1
%282x%28x%2B7%29%2B3%28x-8%29%29%2F%28%28x-8%29%28x%2B7%29%29=1
2x%28x%2B7%29%2B3%28x-8%29=1%28x-8%29%28x%2B7%29
2x%5E2%2B14x%2B3x-24=x%5E2%2B7x-8x-56
2x%5E2%2B17x-24=x%5E2-x-56
2x%5E2%2B17x-24-x%5E2%2Bx%2B56=0
x%5E2%2B18x%2B32=0
x%5E2%2B2x%2B16x%2B32=0
%28x%5E2%2B2x%29%2B%2816x%2B32%29=0
x%28x%2B2%29%2B16%28x%2B2%29=0
%28x%2B2%29%28x%2B16%29+=+0
solutions:
if %28x%2B2%29=+0=>x=-2
if %28x%2B16%29+=+0=>x=-16
check:
=>x=-2
y%5B1%5D+=+2x%2F%28x-8%29=>y%5B1%5D+=+%282%28-2%29%29%2F%28-2-8%29=-4%2F-10=2%2F5
y%5B2%5D+=+3%2F%28x%2B7%29=>y%5B2%5D+=+3%2F%28-2%2B7%29=3%2F5
given condition: y%5B1%5D+%2B+y%5B2%5D+=+1=>2%2F5+%2B+3%2F5=5%2F5+=+1
now you can check for =>x=-16