Question 384329
{{{15y=6+15x}}} Start with the first equation.



{{{15y-6=15x}}} Subtract 6 from both sides.



{{{15x=15y-6}}} Rearrange the equation.



{{{15x-20y=-7}}} Move onto the second equation.



{{{15y-6-20y=-7}}} Replace '15x' with '15y-6'. This is possible because {{{15x=15y-6}}}



{{{-5y-6=-7}}} Combine like terms on the left side.



{{{-5y=-7+6}}} Add {{{6}}} to both sides.



{{{-5y=-1}}} Combine like terms on the right side.



{{{y=(-1)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{y}}}.



{{{y=1/5}}} Reduce.



{{{15x=15y-6}}} Go back to the equation where we isolated 15x



{{{15x=15(1/5)-6}}} Plug in {{{y=1/5}}}



{{{15x=3-6}}} Multiply and reduce.



{{{15x=-3}}} Combine like terms on the right side.



{{{x=(-3)/(15)}}} Divide both sides by {{{15}}} to isolate {{{x}}}.



{{{x=-1/5}}} Reduce.



So the solutions are {{{x=-1/5}}} and {{{y=1/5}}}



which form the ordered pair *[Tex \LARGE \left(-\frac{1}{5},\frac{1}{5}\right)]



So the system is consistent and independent.