Question 203199
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In Eqn 1: {{{x+4y=-6}}}


Let Fy=0:
{{{x+4(0)=-6}}}
{{{red(x=-6)}}}, X-Intercept
Let Fx=0:
{{{0+4y=-6}}} ---> {{{cross(4)y/cross(4)=-6/4}}}
Reduced: {{{red(y=-3/2)}}}, Y-Intercept


In Eqn 2: {{{2x-3y=-1}}}


Let Fy=0:
{{{2x-3(0)=-1}}}
{{{cross(2)x/cross(2)=-1/2}}}
{{{red(x=-1/2)}}}, X-Intercept
Let Fx=0:
{{{2(0)-3y=-1}}}
{{{cross(-3)y/cross(-3)=-1/-3}}}
{{{red(y=1/3)}}}


*For the Point of intersection.

In Eqn 1, we isolate "x": {{{x=-6-4y(red(Eqn3))}}}, subst. in Eqn 2:
{{{2(highlight(-6-4y))-3y=-1}}}
{{{-12-8y-3y=-1}}} ---> {{{-12+1=8y+3y}}} 
{{{-11=11y}}} ---> {{{cross(-11)-1/cross(11)=cross(11)y/cross(11)}}}
{{{highlight(red(y=-1))}}}, subst. in {{{red(Eqn3))}}}


{{{x=-6-4(highlight(-1))=-6+4}}}
{{{highlight(red(x=-2))}}}


*POI = (-2,-1)


We see both lines:
{{{drawing(400,400,-9,5,-5,5,grid(1),graph(400,400,-9,5,-5,5,(-6-x)/4,(2x+1)/3),blue(circle(-6,0,.08)),blue(circle(0,-3/2,.08)),blue(circle(-1/2,0,.08)),blue(circle(0,1/3,.08)),green(circle(-2,-1,.12)),red(circle(-2,-1,.10)))}}} ---><font color=red>Red=Eqn.1</font>; <font color=green>Green=Eqn.2</font>


Thank you,
Jojo</font>