Question 119691

Start with the given system

{{{1y=x-2}}}
{{{y=4x+1}}}




{{{4x+1=x-2}}}  Plug in {{{y=4x+1}}} into the first equation. In other words, replace each {{{y}}} with {{{4x+1}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{4x=x-2-1}}}Subtract 1 from both sides



{{{4x-x=-2-1}}} Subtract x from both sides



{{{3x=-2-1}}} Combine like terms on the left side



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



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




{{{x=-1}}} Divide





Now that we know that {{{x=-1}}}, we can plug this into {{{y=4x+1}}} to find {{{y}}}




{{{y=4(-1)+1}}} Substitute {{{-1}}} for each {{{x}}}



{{{y=-3}}} Simplify



So our answer is {{{x=-1}}} and {{{y=-3}}}