Question 102924
1. {{{10*x+2y=7}}}
2. {{{y=-5*x+3}}}
Use equation (2) and substitute into (1):
2.{{{y=-5*x+3}}}
{{{2*y=2*(-5*x+3)}}}
{{{2*y=2*(-5*x)+2*3}}} Distributive property.
{{{2*y=-10*x+6}}} Simplify.
{{{2*y+10*x=cross(-10*x)+cross(10*x)+6}}} Additive inverse of (-10*x).{{{2*y+10*x=6}}} Simplify.
{{{cross(2*y)-cross(2*y)+10*x=6-2*y}}}Additive inverse of (2*y).
{{{10*x=6-2*y}}}Simplify. 
Use this results in equation (1). 
1. {{{10*x+2y=7}}}
{{{6-cross(2*y)+cross(2y)=7}}}
{{{6=7}}}
Since the equations lead to a false statement, they are inconsistent. 
{{{ graph( 300, 300, -2, 2, -2, 2, -5x+3,-5x+3.5) }}} 
Looking at the graphs of both equations, you see that they have the same slope (parallel) and different intercepts. They will never meet (i.e. have a solution).