Question 65846
Solve

E1)  x^2 + y^2 = 5

E2)  x - 3y = 5  ~~> x=3y+5
Substititute 3y+5 in for x in E1.
{{{(3y+5)^2+y^2=5}}}
{{{9y^2+30y+25+y^2=5}}}
{{{10y^2+30y+25=5}}}
{{{10y^2+30y+25-5=5-5}}}
{{{10y^2+30y+20=0}}}
{{{10(y^2+3y+2)=0}}}
{{{10(y^2+3y+2)/10=0/10}}}
{{{y^2+3y+2=0}}}
{{{(y+2)(y+1)=0}}}
y+2=0 or y+1=0
y=-2 or y=-1
Substitute these values in for y in E2 and solve for x:
x=3(-2)+5  or x=3(-1)+5
x=-6+5 or x=-3+5
x=-1 or x=2
The circle (E1) is intercected by the line (E2) in two places:
(-1,-2) and (2,-1)
Graphically,
{{{graph(300,200,-3.79,3.79,-2.177,2.8225,sqrt(5-x^2),-1*sqrt(5-x^2),(-x+5)/-3)}}}
Happy Calculating!!!