Question 200992
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Given:{{{system(4x-12y=16(red(EQN1)),8x+4y=24(red(EQN2)))}}}


Multiply {{{red(EQN2)}}} by 3 then add to {{{red(EQN1)}}}:
({{{8x+4y=24(red(EQN2))}}})({{{3}}})
{{{red(24x+12y=72)}}}


{{{4x-cross(12y)=16(red(EQN1))}}}
+{{{red(24x+cross(12y)=72)}}}
----------------------------
{{{28x=88}}} ---> {{{cross(28)x/cross(28)=88/28=22/7}}}
{{{highlight(red(x=22/7))}}}, subst. in {{{red(EQN1)}}}


{{{4(highlight(22/7))-12y=16}}}
{{{88/7-16=12y}}}
{{{(88-112)/7=12y}}} ----> {{{-24/7=12y}}} ----> {{{(-24/7)/12=cross(12)y/cross(12)}}}
{{{y=(-24/7*12)=-24/84}}}, divide both by 12
{{{highlight(red(y=-2/7))}}}


*These two lines meet at point <font color=red>(22/7,-2/7) or (3.14,-0.2857)
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In {{{red(EQN1)}}}, let Fy=0:
{{{4x-12y=16}}}
{{{4x-12(0)=16}}} ---> {{{4x=16}}} --->{{{cross(4)x/cross(4)=cross(16)4/cross(4)}}}
{{{x=4}}}, X-Intercept
Let fx=0:
{{{4(0)-12y=16}}}
{{{-12y=16}}} ---> {{{y=16/-12}}} 
{{{y=-4/3}}}, Y-Intercept



In {{{red(EQN2)}}}, let Fy=0:
{{{8x+4y=24}}}
{{{8x+4(0)=24}}} ---> {{{cross(8)x/cross(8)=cross(24)3/cross(8)}}}
{{{x=3}}}, X-Intercept
let Fx=0:
{{{8(0)+4y=24}}} ---> {{{cross(4)y/cross(4)=cross(24)6/cross(4)}}}
{{{y=6}}}, Y-Intercept



{{{drawing(400,400,-8,8,-4,8,graph(400,400,-8,8,-4,8,(4x-16)/12,(24-8x)/4),green(circle(4,0,.12)),green(circle(0,-4/3,.12)),red(circle(3,0,.12)),red(circle(0,6.12)),blue(circle(22/7,-2/7,.15)),red(arrow(-6,-2,-5,-2.8)),red(locate(-6.5,-1.7,EQN1)),green(arrow(2,5,1,4.2)),red(locate(1.8,5.4,EQN2)))}}}


Thank you,
Jojo</font>