Cant solve this equation :(

hey everyone
i was busy doing hardcore physics
when to my surprise i hit these equations in a typically long phy question which i couldnt solve

well I thought i could do linear equations in 3 variables but i couldnt get this

can anyone please do this and tell me how to do these kind of questions?

2y=3x

y= -3z (its negatve of 3z)

x= -2z (negative of 2z again)

thank you everyone
greatly appreciated

This particular system of equations has infinite solutions. The solutions lie on the line that passes through the origin with a direction given by the vector <2,3,-1>.

Essentially, for any value of "t", you can find a solution of the form:

x=2t
y=3t
z=-t