Question 197186
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Given, {{{system(y = 4x-2(red(Line1)),y = 5x(red(Line2)))}}}


In {{{red(Line1)}}}, let Fy=0:
{{{0=4x-2}}} ---> {{{4x=2}}} ---> {{{cross(4)x/cross(4)=cross(2)1/cross(4)2}}}
{{{red(x=1/2)}}}, X-Intercept


Also, Let Fx=0:
{{{y=4(0)-2}}}
{{{red(y=-2)}}}, Y-Intercept


In {{{red(Line2)}}}, ---> {{{y=5x}}}, from the origin (0,0) has a {{{Slope=m=5/1=DELTA(y)/DELTA(x)=rise/run}}} 


We substitute {{{red(Line2)}}} in {{{red(Line1)}}}:
{{{highlight(5x)=4x-2}}}
{{{5x-4x=-2}}}
{{{red(x=-2)}}} ---> Subst. in {{{red(Line2)}}}


{{{y=5*highlight(-2)}}}
{{{red(y=-10)}}}


*The two lines intersect at point (-2,-10)


{{{drawing(400,400,-5,5,-15,8,grid(1),graph(400,400,-5,5,-15,8,4x-2,5x),green(circle(1,5,.12)),green(circle(1,5,.10)),green(circle(-1,-5,.12)),green(circle(-1,-5,.10)),blue(circle(-2,-10,.15)),red(circle(1/2,0,.12)),red(circle(1/2,0,.10)),red(circle(0,-2,.12)),red(circle(0,-2,.10)),green(arrow(-2,-4,-1.1,-4.8)),green(locate(-2.9,-2.2,Slope=5/1)),green(arrow(2,4,1.1,4.8)),green(locate(2,4,Slope=5/1)))}}} --->}}} {{{red(Line1)}}}; {{{green(Line2)}}}



Thank you,
Jojo</font>