5x-10y=25
24x+ay=120
What is this exceptional value for a?

Question

5x-10y=25
24x+ay=120
What is this exceptional value for a?

anonymous · Answer

what the monkey does "exceptional value" mean?

pulsified333 · Answer

no clue

directrix · Answer

The one value of "a" for which the system of equations does NOT have a unique solution.

Exceptional Value as defined elsewhere.

pulsified333 · Answer

so how would i solve for a?

directrix · Answer

I have a candidate for an answer.

directrix · Answer

I took this: 5x-10y=25 and divided each member by the common factor of 5.

x - 2y = 5 which means x = 5 + 2y

In the second equation, 

24x+ay=120

I replaced x by (5 + 2y) as in solving the system by substitution.

directrix · Answer

which led to:

24(5 + 2y)+ay=120

120 + 48 y  + ay = 120

directrix · Answer

The 120 terms subtracted off, leaving

48y + ay = 0

directrix · Answer

Factoring out y:

y * (48 + a) = 0

Then the Zero Product Property

 y = 0  or 48 + a = 0

y = 0 or a = -48

pulsified333 · Answer

you sir are a genius

directrix · Answer

Then, I put the -48 in for a in the original equation. 5x-10y=25 24x - 48y=120 and graphed the two equations. They were the same equation in disguise and the solution is a single line with infinitely many solutions. So, a = -48 is the exceptional value. http://www.wolframalpha.com/input/?i=5x-10y%3D25%2C++24x+-48y%3D120