# Let c be a constant. For what values of c can the simultaneous equations #x-y=2; cx+y=3# have a solution (x, y) inside quadrant l?

##### 2 Answers

In the first quadrant, both

#{(-y = 2 - x), (y = 3 - cx):}#

#-(3 - cx) = 2 - x#

#-3 + cx = 2 - x#

#cx + x = 5#

#x(c + 1) = 5#

#x = 5/(c + 1)#

We need

There will be a vertical asymptote at

Let

So, the solution is

Hence, all values of

Hopefully this helps!

#### Explanation:

The equation

graph{x-2 [-10, 10, -5, 5]}

The other equation is

**(i)** it should have a minimum slope that of line joining

and **(ii)** it should be passing through

Hence, values of

graph{(x-y-2)(x-y+3)(3x+2y-6)=0 [-10, 10, -5, 5]}