Question 188339
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Given{{{system(x-2y=6(EQN1),y=11-3x(EQN2))}}}
Substitute {{{EQN2}}} in {{{EQN1}}}:


{{{x-2(highlight(11-3x))=6}}}
{{{x-22+6x=6}}}
{{{7x=22+6=28}}} ---->{{{cross(7)x/cross(7)=cross(28)4/cross(7)}}}
{{{red(x=4)}}}, substitute in {{{EQN2}}}
{{{y=11-3(highlight(4))=11-12=red(-1)}}}


*These two lines intersect at point <font color=red>(4,-1)</font>


Let's find the intercepts:
In {{{EQN1}}}, 
let fy=0 ---> {{{x-(2)(0)=6}}} ---> {{{red(x=6)}}} , X-Intercept
let fx=0 ---> {{{0-2(y)=6}}} ----> {{{cross(-2)y/cross(-2)=cross(6)-3/cross(-2)}}} ----> {{{red(y=-3)}}}, Y-Intercept


In {{{EQN 2}}},
let fy=o ----> {{{0=11-3x}}} ----> {{{3x=11}}} ---> {{{cross(3)x/cross(3)=11/3}}} ----> {{{red(x=11/3)}}}, X -Intercept
let fx= 0 ---> {{{y=11-3(0)}}} ---> {{{red(y=11)}}}, Y-Intercept


Let' see the graph;
{{{drawing(400,400,-5,10,-5,15,grid(1),graph(400,400,-5,10,-5,15,(x-6)/2,11-3x),blue(circle(4,-1,.18)),green(circle(6,0,.15)),green(circle(0,-3,.15)),circle(11/3,0,.12),circle(0,11,.12))}}} ---> RED, {{{EQN1}}};; GREEN, {{{EQN2}}}


Thank you,
Jojo</font>