Question 187550
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Given Line Eqns{{{system(8x-4y=16(EQN1),5y-10x=3(EQN2))}}}
Multiply EQN 1 by 5: (8x-4y=16)(5)= 40x-20y=80=>{{{cross(40x)-cross(20y)=80}}}
Multiply EQN 2 by 4: (5y-10x=3)(4)= 20y-40x=12=>{{{cross(20y)-cross(40x)=12}}}
Result after addition: {{{0=92}}}
No solution to satisfy given set of condition

Following Slope-Intercept Form to verify{{{system(y=mx+b)}}}
In EQN1 --->{{{4y=8x-16}}}--->{{{cross(4)y/cross(4)=(8x-16)/4}}}
{{{y=(8/4)x-(16/4)=highlight(2)x-4}}}, EQN 1.1
In EQN 2--->{{{5y=10x+3}}}--->{{{cross(5)y/cross(5)=(10x+3)/5}}}
{{{y=(10/5)x+(3/5)=highlight(2)x+3/5}}}, EQN 2.2


*Since the Slope are the same, these Lines are Parallel.

In EQN 1.1, Let fy=0---> {{{0=2x-4}}}--->{{{2x=4}}}--->{{{cross(2)x/cross(2)=cross(4)2/cross(2)}}}
{{{red(x=2)}}}, X-Intercept
Let fx=0---> {{{y=(2)(0)-4=red(-4)}}} Y-Intercept

In EQN 2.2, Let fy=0---> {{{0=2x+3/5}}}--->{{{2x=-3/5}}}--->{{{cross(2)x/cross(2)=(-3/5)/(2)=(-3/5)(1/2)}}}
{{{red(x=-3/10)}}}, X-Intercept
Let fx=0---->{{{y=(2)(0)+3/5=red(3/5)}}}, Y-Intercept


We  graph the lines:
{{{drawing(400,400,-5,10,-5,5,grid(1),graph(400,400,-5,10,-5,5,2x-4,2x+(3/5)),blue(circle(2,0,.12)),blue(circle(0,-4,.12)),blue(circle(2,0,.10)),blue(circle(0,-4,.10)),blue(circle(-3/10,0,.12)),blue(circle(-3/10,0,.10)),blue(circle(0,3/5,.12)),blue(circle(0,3/5,.10)))}}}---> RED (EQN1); GREEN (EQN2)


Thank you,
Jojo</font>