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Solve by cross multiplication method 5ax + 6by = 28 3ax + 4by = 18 |
| Answer» The systems of equations are:5ax + 6by = 28 .......................(i)3ax + 4by = 18 .......................(ii)From (i) and (ii), we geta1 = 5a, b1 = 6b, c1 = -(28)a2 = 3a, b2 = 4b, c2 = -(18)By cross multiplication method, we get{tex}\\frac{x}{{-108b +112b}} = \\frac{{ - y}}{{ - 90a + 84a }} = \\frac{1}{{20ab - 18ab}}{/tex}{tex}\\frac{x}{{4b}} = \\frac{{ - y}}{{ - 6a}} = \\frac{1}{{2ab}}{/tex}Now, {tex}\\frac{x}{{4b}} = \\frac{1}{{2ab}} {/tex}{tex}⇒ x = \\frac{2}{a}{/tex}And, {tex}\\frac{{ - y}}{{ - 6a}} = \\frac{1}{{2ab}} {/tex}{tex}⇒ y = \\frac{3}{b}{/tex}Therefore the solution of the given system of equation is {tex}\\frac{2}{a}{/tex}\xa0and {tex}\\frac{3}{b}{/tex}. | |