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Unfortunately, you actually have three unknowns (K_1, K_2, and V_0) and only two equations. Or, because V_0 is defined as K_1, this problem simplifies to two unknowns (K_1 and K_2) and only one equation. Therefore, there is no single solution. The red K_2 may be Mathcad's way of telling you that you don't have enough equations. I no longer have a version of classic Mathcad, so I can't duplicate your work exactly, but I did set up the Mathcad Prime 9.0 equivalent.
For my worksheet, I made up numbers for i_L, R, α, ω_a, and C. I set up the Solve Block two ways: (1) using your two equations and adding a guess for V_0 and (2) combining the two equations into one and getting rid of V_0. Then I fiddled around with the five variables that I had made up. In the first case, K_1 always equaled the guess value for V_0 (the K_1 guess was irrelevant). In the second case, K_1 always equaled its guess value; I renamed variables and rearranged the longer equation, but K_1 always equaled its guess value. However, I made a second solve block with the K_2 term before the two K_1 terms and now K_2 matched its guess and it was K_1 that changed when I fiddled with i_L, R, α, ω_a, and C.
I think Prime should have returned an error due to insufficient equations, but it appears to be programmed to hold the first variable constant and solve only for the second variable.
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