Question 1137793
{{{4x - y =5}}} 
{{{x}}},{{{y }}}   
{{{0 }}},{{{-5}}} ->  {{{4*0 - y =5}}} -> {{{- y =5}}}->{{{y=-5}}}  
{{{1}}},{{{-1}}}  ->  {{{4*1 - y =5}}} -> {{{4-5 =y}}}->{{{y=-1}}}    
{{{3 }}},{{{7}}}   ->  {{{4*3 - y =5}}} -> {{{12-5 =y}}}->{{{y=7}}}
 
and {{{4x -4y = -4}}}

{{{x}}},{{{y}}}
{{{0}}},{{{1}}}->{{{4*0 -4y = -4}}}->{{{0+4  = 4y}}}->{{{4=4y}}}->{{{y=1}}}
{{{1}}},{{{2}}}->{{{4*1 -4y = -4}}}->{{{4+4  = 4y}}}->{{{8=4y}}}->{{{y=2}}}
{{{-1}}},{{{0}}}->{{{4*(-1) -4y = -4}}}->{{{-4+4  = 4y}}}->{{{0=4y}}}->{{{y=0}}}


plot the points for each line and draw lines through


{{{drawing ( 600, 600, -10, 10, -10, 10,
circle(0,-5,.12),locate(0,-5,p(0,-5)),
circle(1,-1,.12),locate(1,-1,p(1,-1)),
circle(3,7,.12),locate(3,7,p(3,7)),

circle(-1,0,.12),locate(-1,0,p(-1,0)),
graph( 600, 600, -10, 10, -10, 10, 4x-5, x+1)) }}}

Your two lines make up a system of equations. If the graphs of the equations intersect, then there is one solution that is true for both equations. 
When the lines intersect, the point of intersection is the only point that the two graphs have in common.

as you can see from the graph, this system of the equation have a solution, line intersect each other in a point ({{{2}}},{{{3}}})