Question 146773
Start with the given system

{{{x+7y=4}}}
{{{x=8-7y}}}




{{{8-7y+7y=4}}}  Plug in {{{x=8-7y}}} into the first equation. In other words, replace each {{{x}}} with {{{8-7y}}}. Notice we've eliminated the {{{x}}} variables. So we now have a simple equation with one unknown.



{{{8=4}}} Combine like terms on the left side



{{{0=4-8}}}Subtract 8 from both sides



{{{0=-4}}} Combine like terms on the right side



Since this equation is <font size=4><b>never</b></font> true for any y value, this means there are no solutions.



Notice if we graph the two equations, we can see that the two lines are parallel and will never intersect. So this verifies our answer.



{{{ graph( 500, 500, -5, 5, -5, 5, (4-x)/(7), (8-x)/(7)) }}} Graph of {{{x+7y=4}}} (red) and {{{x=8-7y}}} (green)