Question 291008
{{{y=10x+25}}} Start with the first equation.



{{{5x+40=10x+25}}} Plug in {{{y=5x+40}}}



{{{5x=10x+25-40}}} Subtract {{{40}}} from both sides.



{{{5x-10x=25-40}}} Subtract {{{10x}}} from both sides.



{{{-5x=25-40}}} Combine like terms on the left side.



{{{-5x=-15}}} Combine like terms on the right side.



{{{x=(-15)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{x}}}.



{{{x=3}}} Reduce.



{{{y=10x+25}}} Go back to the first equation



{{{y=10(3)+25}}} Plug in {{{x=3}}}



{{{y=30+25}}} Multiply



{{{y=55}}} Add.



So the solutions are {{{x=3}}} and {{{y=55}}} which form the ordered pair *[Tex \LARGE \left(3,55\right)] (ie the two graphs intersect at this point).



This means that the system is consistent and independent.