Question 1152883

let Leah's age be {{{x}}} and Andy’s age {{{y}}}

if the sum of Leah's age and Andy’s age is {{{34}}} we have

{{{x+y=34}}}......eq.1


if {{{5}}} years ago the sum of {{{twice}}} Leah's age and {{{three}}}{{{ times}}} Andy’s age was {{{61 }}}, we have

{{{2(x-5)+3(y-5)=61}}}
{{{2x-10+3y-15=61}}}
{{{2x+3y=61+10+15}}}
{{{2x+3y=86}}}......eq.2


solve the system:

{{{x+y=34}}}......eq.1......both sides multiply by {{{-2}}}
{{{2x+3y=86}}}......eq.2
------------------------------------

{{{-2x-2y=-68}}}......eq.1.
{{{2x+3y=86}}}......eq.2
-------------------------------add both eq.

{{{-2x-2y+2x+3y=-68+86}}}

{{{-cross(2x)-2y+cross(2x)+3y=18}}}

{{{y=18}}}

go to

{{{x+y=34}}}......eq.1, substitute {{{y}}}

{{{x+18=34}}}

{{{x=34-18}}}

{{{x=16}}}


How old are they now?

Leah is {{{16}}} years old now, and Andy is {{{18}}} years old now