Solving for two unknown angles, from two equations.

I am trying to solve for two angles A and B, I have the following two equations
0 = sinA - 1.341sinB and 2 = cosA + 1.341cosB
I have made sinB and cosB the subjects for both equations
sinB = sinA/1.341
cosB = (2-cosA)/1,341
I now know that sin^2 B + cos^2 B = 1
This then means I square both parts and add them together
I get: 1 = Sin^2 A / 1.798 + 2.224 - cos^2 A / 1.798
I guess I can then multiply both sides by 1.798 and get 1.798 = sin^2 A + 2.622 - cos^2 A
Therefore -0.824 = sin^2 A - cos ^2 A
or 0.824 = cos^2 A - sin^2 A
or 0.824 + sin^2 A = cos^2 A
From here I get stuck and I am not sure that I have not already made a mistake.
Can anyone help please, I know the answer to the angles but I want to sse the full working out.
Algebra Trigonometry
Charles Moore Charles Moore
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