Question 179543
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Given{{{system(3x+y=6(EQN1),6x+2y=10 (EQN2))}}}
In EQN 1, we get
{{{y=6-3x(EQN3)}}}, subst. in EQN 2
{{{6x+2(6-3x)=10}}}
{{{6x+12-6x=10}}}---->{{{cross(6x)-cross(6x)=10-12}}}
{{{0=-2}}} ---> This means these 2 Line Eqn's don't INTERSECT, but rather they're PARALLEL.
Via Slope-Intercept Form: {{{y=mx+b}}}
In EQN 3, {{{y=6-3x}}}
Let {{{f(x)=0}}}
{{{y=6-3(0)}}}
{{{highlight(y=6)}}}
Let{{{f(y)=0}}}
{{{0=6-3x}}}
{{{3x=6}}}--->{{{cross(3)x/cross(3)=cross(6)2/cross(3)}}}
{{{highlight(x=2)}}}
In EQN 2:
{{{2y=10-6x}}}--->{{{cross(2)y/cross(2)=(10-6x)/2}}}
{{{y=10/2-(6/2)x=5-3x}}}
Let {{{f(x)=0}}}
{{{y=5-3(0)=highlight(5)}}}
Let{{{f(y)=0}}}
{{{0=5-3x}}}---->{{{3x=5}}}--->{{{cross(3)*x/cross(3)=5/3}}}
{{{highlight(x=5/3)}}}
Let's see the graph:
{{{drawing(400,400,-4,5,-10,10,grid(1),graph(400,400,-4,5,-10,10,6-3x,5-3x),blue(circle(2,0,.10)),blue(circle(0,6,.10)),blue(circle(5/3,0,.10)),blue(circle(0,5,.10)))}}}----->RED>>>> EQN1: GREEN>>>>EQN2
Thank you,
Jojo</pre>