Question 140630
{{{6x+y=4}}} Start with the second equation



{{{y=4-6x}}} Subtract 6x from both sides



{{{y=4x^2-4x+2}}} Move onto the first equation



{{{4-6x=4x^2-4x+2}}} Plug in {{{y=4-6x}}}



{{{0=4x^2-4x+2-4+6x}}}  Subtract 4 from both sides.  Add 6x to both sides. 



{{{0=4x^2+2x-2}}}  Combine like terms



{{{2(x+1)(2x-1)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x+1=0}}} or  {{{2x-1=0}}} 


{{{x=-1}}} or  {{{x=1/2}}}    Now solve for x in each case





So the x-values of the intersections are


 {{{x=-1}}} or  {{{x=1/2}}}