Question 190012
<font face="Tahoma" size=1.5>
</pre><font size=4><b>
Given Line Eqn{{{system(5x-2y=4(red(EQN1)),3x-2y=5(red(EQN2)))}}}


*Note in {{{red(EQN2)}}}, {{{3x-2y-5}}}={{{3x-2y=5}}}


MULTIPLY {{{red(EQN1)}}} by -1 


({{{5x-2y=4}}})x{{{(-1)}}} = {{{-5x+2y=-4}}}, {{{red(EQN3)}}} and ADD {{{red(EQN2)}}}:


{{{-5x+cross(2y)=-4}}}, {{{red(EQN3)}}}
+{{{3x-cross(2y)=5}}}, {{{red(EQN2)}}}
----------------
{{{-2x=1}}} ---> {{{cross(-2)x/cross(-2)=-1/2}}}
{{{highlight(red(x=-1/2))}}},subst. in {{{red(EQN1)}}}


{{{5(highlight(-1/2))-2y=4}}}
{{{-5/2-2y=4}}}
{{{2y=-5/2-4=(-5-8)/2=-13/2}}}
{{{cross(2)y/cross(2)=(-13/2)/2}}}
{{{highlight(red(y=-13/4))}}}


These 2 lines intersect at point (-1/2,-13/4) ---> (-0.50,-3.25)


{{{drawing(400,400,-5,5,-5,5,graph(400,400,-5,5,-5,5,(5x-4)/2,(3x-5)/2),blue(circle(-1/2,-13/4,.08)))}}} ----> {{{red(RED=EQN1)}}}; {{{green(GREEN=EQN2)}}}


Thank you,
Jojo</font>