Question 203999
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Given: {{{system(6x - 9y = 12 (red(EQN1)),4x -6y = 18(red(EQN2)))}}}


Transforming each given line to Slope-Intercept Form,{{{red(y=mx+b)}}}
{{{red(EQN1)}}}:
{{{6x-9y=12}}} ---> {{{6x-12=9y}}} ---> {{{(6x-12)/9=cross(9)y/cross(9)}}}
{{{y=(6/9)x-12/9}}}
{{{y=(2/3)x-4/3}}}


{{{red(EQN2)}}}:
{{{4x-6y=18}}} ---> {{{4x-18=6y}}} ---> {{{(4x-18)/6=cross(6)y/cross(6)}}}
{{{y=(4/6)x-18/6}}} 
{{{y=(2/3)x-3}}}


*The Slope=m of {{{red(EQN1)}}}, {{{y=(highlight(2/3))x-4/3}}} is the same as the one for {{{red(EQN2)}}}, {{{y=(highlight(2/3))x-3}}}.


Therefore, the two lines are PARALLEL.


{{{drawing(400,400,-6,6,-6,6,graph(400,400,-6,6,-6,6,(2/3)x-4/3,(2/3)x-3))}}} ---> {{{red(EQN1)}}}; {{{green(EQN2)}}}


Thank you,
Jojo</font>