Question

x-5y+2z=1,3x-2y+2z=-1

need the set sulotion

Answer 1

this is a system of equations with three variables and two equations, therefore no unique solution is possible. it will have an infinite number of solutions. it is possible to describe all solutions using a parameter t. let x = t:

so t - 5y + 2z = 1

thus 2z = 1 + 5y - t

substitute 2z into the other equation:

3t - 2y + 1 + 5y - t = -1

hence 2t + 3y = -2

hence 3y = -2 - 2t

so y = -2(1 + t)/3

now substitute y back into the equation for 2z:

2z = 1 - 10(1 + t)/3 - t

so 2z = (3 - 10 - 10t - 3t)/3

so 2z = (-7 - 13t)/3

thus z = -(7 + 13t)/6

so the solution can be described as x = t, y = -2(1 + t)/3, z = -(7 + 13t)/6, for all t

Answer 2

thank you my HERO