All published worksheets from http://sagenb.org
EXAMPLE 1 Solve:
x2=2y+10 x^2 = 2y + 10x2=2y+10
3x−y=9 3x - y = 93x−y=9
var('x y') solve([x^2 == 2*y + 10, 3*x - y == 9], [x, y])
f(x) = 3*x - 9 g(x) = (x^2 - 10)/2 show(plot(f, -4, 5)+plot(g, -4, 5), ymin = -9, aspect_ratio = 1)
EXAMPLE 2 Solve:
x−y=3 x - y = 3x−y=3
(x−2)2+(y+3)2=4 (x - 2)^2 + (y + 3)^2 = 4(x−2)2+(y+3)2=4
var('x y') solve([x-y == 3, (x-2)^2 + (y+3)^2 == 4], [x,y])
f(x) = x - 3 g(x) = sqrt(4 - (x-2)^2) - 3 h(x) = -sqrt(4 - (x-2)^2) - 3 show(plot(f, -1, 4) + plot(g, 0, 4)+plot(h, 0, 4), aspect_ratio = 1)
EXAMPLE 3 Solve:
4x2+y2=134x^2 + y^2 = 134x2+y2=13
x2+y2=10 x^2 + y^2 = 10x2+y2=10
var('x y') solve([4*x^2 + y^2 == 13, x^2 + y^2 == 10], [x, y])
f1(x) = sqrt(13 - 4*x^2) f2(x) = -sqrt(13 - 4*x^2) g1(x) = sqrt(10 - x^2) g2(x) = -sqrt(10 - x^2) show(plot(f1, -sqrt(13)/2, sqrt(13)/2) + plot(f2, -sqrt(13)/2, sqrt(13)/2) + plot(g1, -sqrt(10), sqrt(10)) + plot(g2, -sqrt(10), sqrt(10)))
EXAMPLE 4 Solve:
y=x2+3 y = x^2 + 3y=x2+3
x2+y2=9 x^2 + y^2 = 9x2+y2=9
var('x y') solve([y == x^2+3, x^2+y^2==9], [x, y])
f(x) = x^2 + 3 g1(x) = sqrt(9-x^2) g2(x) = -sqrt(9-x^2) show(plot(f, -3, 3)+plot(g1, -3, 3)+plot(g2, -3, 3), aspect_ratio = 1)
EXAMPLE 5
2x+2y+y=362x + 2y + y = 362x+2y+y=36
xy=54 xy = 54xy=54
var('x y') solve([2*x+3*y == 36, x*y == 54], [x, y])
f(x) = (36-2*x)/3 g(x) = 54/x plot(f, 0, 20)+plot(g, 1, 54)