Question 919405


thinking of two numbers:{{{x}}} and {{{y}}}


 when i double  the first and add it to the second the total is thirteen:

{{{2x+y=13}}}.......eq.1

 when i double the second and take it away from the first i get minus one: 

{{{x-2y=-1}}}.......eq.2

solve the system:

{{{2x+y=13}}}.......eq.1
{{{x-2y=-1}}}.......eq.2....both sides multiply by {{{2}}}
_________________________________

{{{2x+y=13}}}.......eq.1
{{{2x-4y=-2}}}.......eq.2
______________________________________subtract eq.2 from eq.1

{{{2x+y-(2x-4y)=13-(-2)}}}

{{{2x+y-2x+4y=13+2}}}

{{{cross(2x)+y-cross(2x)+4y=15}}}

{{{y+4y=15}}}

{{{5y=15}}}

{{{y=15/5}}}

{{{y=3}}}

now find {{{x}}}

{{{x-2y=-1}}}.......eq.2..plug in {{{3}}} for {{{y}}}

{{{x-2*3=-1}}}

{{{x-6=-1}}}

{{{x=-1+6}}}

{{{x=5}}}

so, your numbers are: {{{x=5}}} and {{{y=3}}}