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    we know that, if Y=a+bX :

    b=Y_mean - slope*X_mean

    So:

    Eq1=> X=5/4Y-30/3 => -30/4 = X_mean-5/4Y_mean

    Eq2=>Y=20/9X-107/9=> -107/9 =Y_mean-20/9X_Mean

    Solve system of Two equations: 33=5Y_mean-4X_mean 107=20X_mean-9Ymean

    X=13 , Y=17