Question 504909
a) only one solution ,(5,1) ****instead of (2,3)
Lets use point slope intercept equation 
let's say the slope is -2.
So,
{{{(y-y1)=m(x-x1) }}}
{{{(y-1)=-2(x-5)}}}
{{{y-1=-2x+10}}}
{{{y=-2x+11}}}----Eq1


For next equation:
Lets use point slope intercept equation 
let's say the slope is 2.


{{{y-y1=m(x-x1)}}}
{{{y-1=2(x-10)}}}
{{{y=2x-9}}} ----Eq2


Next lets check


Lets substitute 
{{{y=2x-9}}} in eq 1
{{{y=-2x+11}}}

So,
{{{2x-9=-2x+11}}}
{{{4x=11+9}}}
{{{4x=20}}}
{{{x=5}}}

Next lets substitute x=5 in eq 
{{{y=2(5)-9}}}
{{{y=10-9}}}
{{{y=1}}}


Therefore eqs are 
{{{y=-2x+11}}}----Eq1
{{{y=2x-9}}} ----Eq2


----------------------
For NO SOLUTION

REmember:
No solution happens when two graphs are parallel. It looks like this (0=7) 
To make lines Paralel we have to have equal slopes.

Lets use the point slope equation  
Lets choose points (3,2) and slope as 4.

{{{y-y1=m(x-x1)}}}
{{{y-3=4(x-2)}}}
{{{y=4x-8+3}}}
{{{y=4x-5}}}    ----eq1


Lets use the point slope equation  again 
This time lets choose points (2,1) and slope as 4.

{{{y-y1=m(x-x1)}}}
{{{y-1=m(x-2)}}}
{{{y=4x-8+1}}}
{{{y=4x-7}}} ----eq2

Lets check:
y=4x-5
y=4x-7
Substitute y=4x-7 in eq y=4x-5
{{{4x-7=4x-5}}}
{{{4x-4x=-5+7}}}
{{{0=2}}}


c)infinite number of solutions 
All that you need to do here is to write an equation and make a second equation a multiple
of the first equation. Example:
.
The first equation is y = 2x +1 ---eq1
.
The second equation is 2y = 4x + 2 ---eq2
.
This 2nd  equ  is just 2 times the 1st eq. 
 So this makes both eq the same they will have the same graph(1 line on the graph. So, these two eqns will have an infinite number of common 
solns.