Can I generate multiple (random) vectors [x1, x2, x3, x4, x5] where all x's are positive numbers such that they all satisfy the linear constraints:

x1+2.x2+6.x3+4.x4+2.x5=10

3.x1+x2+4.x3+7.x4+4.x5=16

Can I for example generate 100 instances of [x1, x2, x3, x4, x5]? And how?