Question 112068

Start with the given system

{{{y-x=86}}}
{{{y=5x-6}}}




{{{(5x-6)-x=86}}}  Plug in {{{y=5x-6}}} into the first equation. In other words, replace each {{{y}}} with {{{5x-6}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{5x-6-x=86}}} Distribute



{{{4x-6=86}}} Combine like terms on the left side



{{{4x=86+6}}}Add 6 to both sides



{{{4x=92}}} Combine like terms on the right side



{{{x=(92)/(4)}}} Divide both sides by 4 to isolate x




{{{x=23}}} Divide





Now that we know that {{{x=23}}}, we can plug this into {{{y=5x-6}}} to find {{{y}}}




{{{y=5(23)-6}}} Substitute {{{23}}} for each {{{x}}}



{{{y=109}}} Simplify



So our answer is {{{x=23}}} and {{{y=109}}}