Question 147313

Start with the given system of equations:

{{{system(2x - 6y = 42,3x - 9y = -15)}}}



{{{3(2x - 6y )=3( 42)}}} Multiply the both sides of the first equation by 3.



{{{6x-18y=126}}} Distribute and multiply.



{{{-2(3x - 9y )=-2( -15)}}} Multiply the both sides of the second equation by -2.



{{{-6x+18y=30}}} Distribute and multiply.



So we have the new system of equations:

{{{system(6x-18y=126,-6x+18y=30)}}}



Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:



{{{(6x-18y)+(-6x+18y)=(126)+(30)}}}



{{{(6x+-6x)+(-18y+18y)=126+30}}} Group like terms.



{{{0x+0y=156}}} Combine like terms. Notice how the x and y terms cancel out.



{{{0=156}}}Simplify.



Since {{{0=156}}} is <font size="4"><b>never</b></font> true, this means that there are no solutions. So the system is inconsistent.