Question 110097
7)                 
{{{y=6-x }}}.....substitute {{{y}}} in second expression            
{{{2x-3y=22 }}}            

{{{2x -3(6 - x)= 22 }}}            
{{{2x -18 + 6x= 22 }}} 
{{{8x -18 = 22 }}}....move {{{-18}}} to the right            
{{{8x = 22 + 18 }}}
{{{8x = 40 }}}..divide both sides by {{{8}}}
{{{x = 5 }}}
           
now find {{{y}}}
{{{y=6-x }}}
{{{y=6-5 }}}
{{{y= 1 }}}

13) 

{{{4x+5y=5}}}....both sides multiply by {{{6}}}
{{{6x+7y=7}}}....both sides multiply by {{{-4}}}
  
{{{24x+30y=30}}}
{{{-24x-28y=-28}}}......now add them

{{{24x +(-24x) + 30y +(-28y) = 30 + (-28)}}}

{{{2y = 2}}}

{{{y = 1}}}

then find {{{x}}}

{{{4x+5y=5}}}

{{{4x + 5*1 = 5}}}

{{{4x = 5 - 5}}}

{{{4x = 0}}}........since {{{4}}}is {{{not_ equal_ to_0}}}, then {{{x_must_be_= 0}}}


15)

{{{x+9y=4}}}...both sides in this equation multiply by {{{-2}}}
{{{2x+3y=7}}}

{{{-2x- 18y=-8}}}....... add both equations
{{{2x+3y=7}}}

{{{-2x +2x -18y + 3y =-8 + 7}}}
{{{-15y = - 1}}}
{{{y = -1/-15}}}
{{{y = 1/15}}}

then find {{{x}}}
{{{x+9y=4}}}
{{{x+9(1/15)=4}}}...
{{{x+9/15=4}}}...
{{{x+(9:3)/(15:3)=4}}}...
{{{x+3/5=4}}}.........move {{{3/5}}} to the right
{{{x = 4 - 3/5}}}
{{{x = 20/5 - 3/5}}}
{{{x = 17/5}}}
{{{x = 3(2/5)}}}