SOLUTION: x + ay = 3 2x + 5y = b for which values of a does each system have a unique solution, and for which pairs of values (a,b) does each system have more than one solution?

Algebra ->  Linear-equations -> SOLUTION: x + ay = 3 2x + 5y = b for which values of a does each system have a unique solution, and for which pairs of values (a,b) does each system have more than one solution?      Log On


   

Question 983796: x + ay = 3
2x + 5y = b
for which values of a does each system have a unique solution, and for which pairs of values (a,b) does each system have more than one solution?
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Try to put these in more the same form than they are currently.

2x%2B5y=b
2x%2F2%2B5y%2F2=b%2F2
x%2B%285%2F2%29y=b%2F2

If the slope of the "3" equation is the same as the slope of the "b" equation, then the two lines are parallel and potentially have no common solution, meaning no intersection. The two lines will meet if a%3C%3E5%2F2.

IF a=5%2F2 AND b%2F2=3, then the two lines have more than one common solution, because they would be the same line. This would mean b=6.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Put both equations into slope-intercept form.





In order for there to be a unique solution, the slopes of the two lines must be different, hence any value of that is NOT equal to will result in a unique solution.

In order for there to be more than one solution, the slopes AND the -intercepts must be equal, hence

John

My calculator said it, I believe it, that settles it