The purpose of this paper is simply to present to the mathematics community a novel approach of solving systems of linear equations in two and three variables. This method uses products of coefficients with determinants and constants with determinants. The method is derived through the cross multiplication of equations which results in finding the critical values (Dx, Dy and Dz). These critical values are later substituted in any initial given equation for the purpose of finding scale factor K. It is this scale factor that is multiplied with critical values to find real solutions. The analysis of this formula shows that it is certainly accurate for all problems it is invented for. Unlike the Crammer’s rule, substitution method, elimination method that requires three and four determinants to solve a two and three variable problems of linear systems of equations, for this method the two and three variable problems only two and three determinants respectively. In two variables In three variables x= (c1Dx)/M x=(d2Dx)/M y=(c1Dy)/M y=(d2Dy)/M z=(d2Dz)/MCoefficients an,bn,cn and constants is obtained from any of the single equation. The ratio method is formally derived and proven in the methodology section and Denominator (M) =a1Dx+ b1Dy for a two variable equations and M=a1Dx+ b1Dy+ c1Dz for 3 variable equations.Keywords: Linear systems of equations, Ratios, Critical Values, Scale factor K, Crammer’s rule, elimination method, substitution method.