Question 950050
Line 1 
{{{x}}}|{{{ y }}}
{{{-4}}}|{{{ 8 }}}
{{{4}}}|{{{ 6}}} 
 
*[invoke change_this_name10094 -4, 8, 4, 6]

Line 2 
 
{{{x}}}|{{{ y }}}
{{{-1}}}|{{{ 1 }}}
{{{3}}}|{{{ 5}}} 

first find equations of the given lines:

*[invoke change_this_name10094 -1, 1, 3, 5]

so, your system is:

{{{y=-0.25x + 7}}}........eq.2
{{{y=x + 2}}}........eq.2

_______________________left sides are equal, then right sides are equal too

{{{x + 2=-0.25x + 7}}}...solve for {{{x}}}

{{{x + 0.25x= 7-2}}}

{{{1.25x= 5}}}

{{{x= 5/1.25}}}

{{{x= 500/125}}}

{{{highlight(x= 4)}}}

now find {{{y}}}

{{{y=x + 2}}}........eq.2

{{{y=4+ 2}}}

{{{highlight(y=6)}}}

these two lines intersecting in one point and it is ({{{4}}},{{{6}}})

{{{ graph( 600, 600, -10, 10, -10, 10, x+2, -0.25x + 7) }}}

so,the answer to the question how many solutions does this system of equations have is:
 B.
{{{exactly}}} {{{1}}}