Question 59854
Solve by any method

E1: -4x+3y=2
E2: 5x-2y=-3
I'm going to use the elimination method in an attempt to avoid fractions.  Multiply E1 by 5 and E2 by 4.  Add E1+E2 to eliminate the x's.
E1:  5(-4x+3y)=5(2) ---> -20x+15y=10
E2:  4(5x-2y)=4(-3) --->  20x-8y=-12
:
-20x+15y=10
20x-8y=-12
__________
0+7y=-2
7y/7=-2/7
y=-2/7  Darn!  It's a fraction anyway.
Substitute -2/7 into either equation for y and solve for x.
{{{-4x+3(-2/7)=2}}}
{{{-4x-6/7=2}}}
{{{7(-4x-6/7)=7(2)}}}  Let's clear the fraction by multiplying everything by 7.
{{{-28x-42/7=14}}}
{{{-28x-6=14}}}
{{{-28x-6+6=14+6}}}
{{{-28x=20}}}
{{{-28x/-28=20/-28}}}  20/-28 reduces by 4.
{{{x=5*4/(-7*4)}}}
{{{x=-5/7}}}
The soltuion is: (-5/7,-2/7)
Happy Calculating!!!