Question 407967
{{{2x-3y+1=0}}} and {{{4y+ 3x +2=0}}}


slope-intercept form:

{{{y=(2/3)x+1/3}}} and {{{y= -(3/4)x -1/2}}}

graph:

{{{ graph( 500, 500, -5, 5, -5, 5, (2/3)x+1/3, -(3/4)x -1/2) }}}

The point (x, y) where they meet must lie on both lines, so {{{x}}} and {{{y}}} must satisfy both equations. 
So we are looking to solve the two simultaneous equations 

{{{y=(2/3)x+1/3}}} and {{{y= -(3/4)x -1/2}}}... left sides are same, so right sides must be same too

{{{(2/3)x+1/3=-(3/4)x -1/2}}}...solve for {{{x}}}

{{{(2/3)x+(3/4)x=-1/3 -1/2}}}

{{{x(2/3+3/4)= -1/3 -1/2}}}

{{{x(8+9)/12= (-2-3)/6}}}

{{{17x= cross(12)2(-5)/cross(6)}}}

{{{17x= 2(-5)}}}

{{{17x= -10}}}

{{{x= -10/17}}}

{{{x= -0.59}}}


{{{y=(2/3)(-0.59)+1/3}}}

{{{y=-0.39+0.33}}}

{{{y=-0.06}}}



The point (x, y) is (-0.59, -0.06)

check:

{{{2x-3y+1=0}}}

{{{2(-0.59)-3(-0.06)+1=0}}}

{{{-1.18+0.18 +1=0}}}

{{{-1+1=0}}}

{{{0=0}}}.......{{{x}}} and {{{y}}} must satisfy this equation...check the other one