Question

solve each system of equation algebraically:
x2+y2=18
x+y=4

Answer 1

Do you mean the circle
x^2+y^2 = 18 ?

Answer 2

yes

Answer 3

Making that assumption, we are looking for where the straight line:
y = -1x + 4
which has a slope of -1 and goes through (0,4) and (4,0)
hits the circle with center at the origin and radius 3 sqrt 2 which is about 4.24
Sketch a graph so we will get an idea of how the solution should look.
So
substitute y = -x + 4 into the circle
x^2 + (-x+4)^2 = 18
x^2 + x^2 - 8 x + 16 = 18
2 x^2 -8 x -2 = 0
x^2 - 4 x -1 = 0
x = (1/2)[ 4 +/- sqrt (16 +4)]
x = (1/2) [ 4 +/- 2 sqrt 5]
x = 2 +/- sqrt 5
find the y for each of those x values