Question 215116
{{{(1/2)x-3y=1}}} Start with the second equation.



{{{x-6y=2}}} Multiply EVERY term by the LCD 2 to clear out the fraction.



So we have the system of equations:



{{{system(x-y=17,x-6y=2)}}}



{{{x-y=17}}} Start with the first equation.



{{{-y=17-x}}} Subtract {{{x}}} from both sides.



{{{y=(17-x)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{y}}}.



{{{y=x-17}}} Rearrange the terms and simplify.



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{{{x-6y=2}}} Move onto the second equation.



{{{x-6(x-17)=2}}} Now plug in {{{y=x-17}}}.



{{{x-6x+102=2}}} Distribute.



{{{-5x+102=2}}} Combine like terms on the left side.



{{{-5x=2-102}}} Subtract {{{102}}} from both sides.



{{{-5x=-100}}} Combine like terms on the right side.



{{{x=(-100)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{x}}}.



{{{x=20}}} Reduce.



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Since we know that {{{x=20}}}, we can use this to find {{{y}}}.



{{{x-y=17}}} Go back to the first equation.



{{{1(20)-y=17}}} Plug in {{{x=20}}}.



{{{20-y=17}}} Multiply.



{{{-y=17-20}}} Subtract {{{20}}} from both sides.



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



{{{y=(-3)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{y}}}.



{{{y=3}}} Reduce.



So the solutions are {{{x=20}}} and {{{y=3}}}.



This means that the system is consistent and independent.