Question 202098


Start with the given system of equations:



{{{system(3x - y = 5,-6x + 2y = 1)}}}



{{{3x - y = 5}}} Start with the first equation.



{{{-y=5-3x}}} Subtract {{{3x}}} from both sides.



{{{y=(5-3x)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{y}}}.



{{{y=3x-5}}} Rearrange the terms and simplify.



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{{{-6x + 2(3x-5) = 1}}} Now plug in {{{y=3x-5}}} into the second equation.



{{{-6x+6x-10=1}}} Distribute.



{{{0x-10=1}}} Combine like terms on the left side.



{{{0x=1+10}}} Add {{{10}}} to both sides.



{{{0x=11}}} Combine like terms on the right side.



{{{0=11}}} Simplify.



Since this equation is <font size=4><b>NEVER</b></font> true for any "x" value, this means that there are no solutions.



So the system is inconsistent.