Question 124559

Start with the given system

{{{2x-5y=-3}}}
{{{y=-4x+1}}}




{{{2x-5(-4x+1)=-3}}}  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.



{{{2x+20x-5=-3}}} Distribute



{{{22x-5=-3}}} Combine like terms on the left side



{{{22x=-3+5}}}Add 5 to both sides



{{{22x=2}}} Combine like terms on the right side



{{{x=(2)/(22)}}} Divide both sides by 22 to isolate x




{{{x=1/11}}} Reduce





Now that we know that {{{x=1/11}}}, we can plug this into {{{y=-4x+1}}} to find {{{y}}}




{{{y=-4(1/11)+1}}} Substitute {{{1/11}}} for each {{{x}}}



{{{y=7/11}}} Simplify



So our answer is {{{x=1/11}}} and {{{y=7/11}}} which also looks like *[Tex \LARGE \left(\frac{1}{11},\frac{7}{11}\right)]