Solve the following systems of equations.
|x|+2|y|=3,5y+7x=2
Given,
|x|+2|y|=3 (equation 1)
5y+7x=2 (equation 2)
From equation 1,
for x>0,y>0
x+2y=3
7x+5y=2
for x<0,y>0
−x+2y=3
⇒x−2y+3=0
for x<0,y<0
x+2y+3=0
for x>0,y<0
x−2y=3
Actually, the graph of above obtained looks like above figure
But as we restricted our domain accordingly as x<0 (or) x>0 and y<0 (or) y>0
The actual solutions are the point of intersection of lines at B and D
Solving 7x+5y=2 (equation 3)
and x−2y+3=0
⇒7x−14y+21=0 (equation 4)
from equation 4 and 5
19y=23
y=2319,x=−7719
Solving x−2y=3 and 7x+5y=2
⇒y=−1x=1
Solutions are (1,−1) and (−7719,2319)