Ball collision momentum problem

1. The problem statement, all variables and given/known data

Hello. I was solving this problem about two balls in a plane colliding elastically. The first one had mass 100g radius 5cm and started with velocity of 3m/s to the right and hit the second ball with mass 50g radius 3cm(initially stationary). It hit the second ball such that the line directed by the velocity vector of the first ball going through the center of the first ball and the line parallel to it going through the center of the second ball (these two lines) are separated by a distance of 1cm.

2. Relevant equations

Conservation of energy AND conservation of momentum

3. The attempt at a solution

Well I started to identify the angles after the collision and I came up with the these angles:
first ball:
cos(alpha’)=1/8; 0<=alpha'<=pi/2
and the second ball:
sin(alpha)=1/8; 0<=alpha<=pi/2
where alpha’ is the angle above the x-axis to the velocity vector of the first ball and alpha is the angle below the x-axis to the velocity vector of the second ball.
Now all we need are the magnitudes of the velocity vectors after the collision. Because it is an elastic collision the energy is conserved and the momentum is conserved. So for energy we have
18=2|v1|^2+|v2|^2
And for the momentum we have
2*v0=2*v1+v2
2<3;0>=2a<cos(alpha’);sin(alpha’)>+b<cos(alpha);-sin(alpha)>
where a,b are the magnitudes of the vectors.

But this system has no solution. Where is the problem? Thank you!

Attached Images
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