Question 187386
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Given{{{system(2x-3y =18 (EQN1),5x +3y =3(EQN2))}}}
In EQN 1 we get:
{{{3y=2x-18}}}---->{{{cross(3)y/cross(3)=(2x-18)/3}}}
{{{y=(2/3)x-(18/3)=(2/3)x-6}}} EQN 3, subst. in  EQN 2:
{{{5x+3(highlight((2/3)x-6))=3}}}
{{{5x+(6/3)x-18=3}}}---->{{{5x+2x-18=3}}}---->{{{7x=3+18=21}}}--->{{{cross(7)x/cross(7)=21/7=3}}}
{{{red(x=3)}}}, Subst. in EQN 3:
{{{y=(2/cross(3))(cross(3))-6=2-6=-4}}}
{{{red(y=-4)}}}
Therefore, point of Intersection (3,-4)
We see graph:
{{{drawing(400,400,-5,10,-10,10,grid(1),graph(400,400,-5,10,-10,10,(2/3)x-6,(-5/3)x+1),blue(circle(3,-4,.12)))}}}--> RED Line (EQN 1); GREEN Line (EQN 2)
Thank you,
Jojo</font>