Question 143104
Start with the given system

{{{-x+y=0}}}
{{{y=4x+5}}}




{{{-x+(4x+5)=0}}}  Plug in {{{y=4x+5}}} into the first equation. In other words, replace each {{{y}}} with {{{4x+5}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{3x+5=0}}} Combine like terms on the left side



{{{3x=0-5}}}Subtract 5 from both sides



{{{3x=-5}}} Combine like terms on the right side



{{{x=(-5)/(3)}}} Divide both sides by 3 to isolate x




{{{x=-5/3}}} Reduce





Now that we know that {{{x=-5/3}}}, we can plug this into {{{y=4x+5}}} to find {{{y}}}




{{{y=4(-5/3)+5}}} Substitute {{{-5/3}}} for each {{{x}}}



{{{y=-20/3+5}}} Multiply



{{{y=-5/3}}} Combine like terms



So our answer is {{{x=-5/3}}} and {{{y=-5/3}}} which forms the point *[Tex \LARGE \left(-\frac{5}{3},-\frac{5}{3}\right)]