Here, a, b, and c are non – zero coefficients, d is a constant. The general form of equations in this form is ax + by + cz = d. System of Equations in Three VariablesĪ relationship between three variables shown in the form of a system of three equations is a triplet of simultaneous equations. Or, x = 10 and solving for y, we have y = 6. Multiplying (i) by (−1) and (ii) by (1), and then subtracting the new equations we have, Subtracting the two equations thus formed gives the required answer. In this method we cross – multiply the equations with respective coefficients. We have, 16 – y = 4 + y or, 12 = 2y or, y = 6 and solving for x, we have x = 10. In other words, two linear equations are reduced to form only one linear equation by eliminating one of the unknowns. In this method, we eliminate one of the variables (say x) from the equation. These values of the variables are the roots of the equations. Methods of Solving a System of Equations in Two VariablesĪ value of each of the unknown or variable satisfies both the equation simultaneously.
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