1207.sagews

EXAMPLE 2  Solving  a System in Three Variables

Solve:

$5x - 2y - 4z = 3$

$3x + 3y + 2z = -3$

$-2x + 5y + 3z = 3$

var('x y z')

solve([5*x - 2*y - 4*z == 3, 3*x + 3*y + 2*z == -3, -2*x + 5*y + 3*z == 3], [x, y, z])

var('x y z')

eq1 = 5*x - 2*y - 4*z == 3
eq2 = 3*x + 3*y + 2*z == -3
eq3 = -2*x + 5*y + 3*z == 3

eq4 = eq1 + 2*eq2
eq4

eq5 = -3*eq2 + 2*eq3
eq5

eq6 = eq4 - 4*eq5
eq6

x = -1

y = 15 + 13*x     # eq5

z = (3 + 2*x - 5*y)/3

x, y, z

var('x y z')

a1, b1, c1, d1 = 1, 0, 1, 3
a2, b2, c2, d2 = 1, 2, -1, 1
a3, b3, c3, d3 = 2, -1, 1, 3

eq1 = a1*x + b1*y + c1*z == d1
eq1

eq2 = a2*x + b2*y + c2*z == d2
eq2

eq3 = a3*x + b3*y + c3*z == d3
eq3

eq4 = c2*eq1 - c1*eq2
eq4

eq5 = c3*eq2 - c2*eq3
eq5

eq6 = eq4/2+eq5
eq6

x = 1
y = 4-3*x
z = 3 - 2*x + y
x, y, z