Question 202053
You're on the right track. You just need to finish up.




Start with the given system of equations:

{{{system(4x+8y=6,3x-8y=7)}}}



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



{{{(4x+8y)+(3x-8y)=(6)+(7)}}}



{{{(4x+3x)+(8y-8y)=6+7}}} Group like terms.



{{{7x+0y=13}}} Combine like terms.



{{{7x=13}}} Simplify.



{{{x=(13)/(7)}}} Divide both sides by {{{7}}} to isolate {{{x}}}.



------------------------------------------------------------------



{{{4x+8y=6}}} Now go back to the first equation.



{{{4(13/7)+8y=6}}} Plug in {{{x=13/7}}}.



{{{52/7+8y=6}}} Multiply.



{{{cross(7)(52/cross(7))+7(8y)=7(6)}}} Multiply EVERY term by the LCD {{{7}}} to clear any fractions.



{{{52+56y=42}}} Multiply and simplify.



{{{56y=42-52}}} Subtract {{{52}}} from both sides.



{{{56y=-10}}} Combine like terms on the right side.



{{{y=(-10)/(56)}}} Divide both sides by {{{56}}} to isolate {{{y}}}.



{{{y=-5/28}}} Reduce.



So the solutions are {{{x=13/7}}} and {{{y=-5/28}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{13}{7},-\frac{5}{28}\right)].



This means that the system is consistent and independent.