Question 189289
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Given:{{{system(-4x+y=-11(EQN1),2x-3y=5(EQN2))}}}


Isolate "y" in EQN 1 ,{{{y=4x-11}}}, EQN 3 (subst. in EQN 2)


{{{2x-3(highlight(4x-11))=5}}}
{{{2x-12x+33=5}}}
{{{-10x=5-33}}}
{{{-10x=-28}}} -----> {{{cross(-10)x/cross(-10)=cross(-28)2.8/cross(-10)}}}
{{{red(x=2.8)}}}, subst. in EQN 3


{{{y=4(highlight(2.8))-11=11.2-11=red(0.2)}}}


Let's check, subst. (x,y) = (2.8,0.20) in EQN 1:
{{{-4(2.8)+0.20=-11}}}
{{{-11.2+0.20=-11}}}
{{{-11=-11}}}, good


Subst. (x,y)=(2.8,0.20) in EQN 2:
{{{2(2.8)-3(0.20)=5}}}
{{{5.6-0.60=5}}}
{{{5=5}}}, good.


These two lines intersect @ point <font color=blue>(2.8, 0.2)</font>


Let's see the graph,
{{{drawing(400,400,-4,4,-4,4,graph(400,400,-4,4,-4,4,4x-11,(2x-5)/3),blue(circle(2.8,.2,.08)))}}} ---><font color=red>RED, EQN 1</font>; <font color=green>GREEN, EQN 2</font>


Thank you,
Jojo</font>