Question 372695
1.{{{2x^2+4y=13}}}
2.{{{x^2-y^2=7/2}}}
Multiply eq. 2 by (-2) and add to eq. 1,
{{{2x^2+4y-2x^2+2y^2=13-7}}}
{{{2y^2+4y=6}}}
{{{y^2+2y-3=0}}}
{{{(y+3)(y-1)=0}}}
Two solutions:
{{{y+3=0}}}
{{{highlight(y=-3)}}}
Then from eq. 1,
{{{2x^2-12=13}}}
{{{2x^2=25}}}
{{{x^2=25/2}}}
{{{highlight(x=0 +- (5/2)sqrt(2))}}}
.
.
.
{{{y-1=0}}}
{{{highlight_green( y=1)}}}
Then from eq. 1,
{{{2x^2+4=13}}}
{{{2x^2=9}}}
{{{x^2=9/2}}}
{{{highlight_green( x=0 +- (3/2)sqrt(2))}}}
.
.
.
{{{drawing(300,300,-6,6,-6,6,grid(1),
circle((3/2)sqrt(2),1,0.3),
circle(-(3/2)sqrt(2),1,0.3),
circle((5/2)sqrt(2),-3,0.3),
circle(-(5/2)sqrt(2),-3,0.3),
graph(300,300,-6,6,-6,6,0,(13-2x^2)/4,sqrt(x^2-7/2)),
graph(300,300,-6,6,-6,6,0,(13-2x^2)/4,-sqrt(x^2-7/2)))}}}
.
.
.
X
XX
XXXXXXXX
XXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXXXXXX
XXXXXXXX
XX
X
.
.
.
1.{{{x^2-y^2=1}}} 
2.{{{2x^2-y^2=x+3}}}
Subtract eq. 1 from eq. 2,
{{{2x^2-y^2-x^2+y^2=x+3-1}}}
{{{x^2=x+2}}}
{{{x^2-x-2=0}}}
{{{(x-2)(x+1)=0}}}
Two solutions:
{{{x-2=0}}}
{{{highlight(x=2)}}}
Then from eq. 1,
{{{4-y^2=1}}}
{{{y^2=3}}}
{{{highlight(y=0 +- sqrt(3))}}}
.
.
.
{{{x+1=0}}}
{{{highlight_green(x=-1)}}}
Then from eq. 1,
{{{1-y^2=1}}}
{{{y^2=0}}}
{{{highlight_green(y=0)}}}
.
.
.
{{{drawing(300,300,-4,4,-4,4,grid(1),

circle(-1,0,0.13),
circle(2,sqrt(3),0.13),
circle(2,-sqrt(3),0.13),
graph(300,300,-4,4,-4,4,0,sqrt(x^2-1),sqrt(2x^2-x-3)),
graph(300,300,-4,4,-4,4,0,-sqrt(x^2-1),-sqrt(2x^2-x-3)))}}}
.
.
.