Question 181877

Start with the given system

{{{4x-5y=-7}}}
{{{y=5x}}}






{{{4x-5(5x)=-7}}}  Plug in {{{y=5x}}} into the first equation. In other words, replace each {{{y}}} with {{{5x}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{4x-25x=-7}}} Distribute



{{{-21x=-7}}} Combine like terms on the left side



{{{x=(-7)/(-21)}}} Divide both sides by -21 to isolate x




{{{x=1/3}}} Reduce





Now that we know that {{{x=1/3}}}, we can plug this into {{{y=5x}}} to find {{{y}}}




{{{y=5(1/3)}}} Substitute {{{1/3}}} for each {{{x}}}



{{{y=5/3}}} Multiply



So our answer is {{{x=1/3}}} and {{{y=5/3}}} which also looks like *[Tex \LARGE \left(\frac{1}{3},\frac{5}{3}\right)]