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Draw a graph of equation1. x+3y=6 2x-3y=12 |
| Answer» Graph of the equation {tex}x + 3y = 6{/tex}:We have, {tex}x + 3y = 6{/tex}{tex} \\Rightarrow {/tex}\xa0{tex}x = 6 - 3y{/tex}When y = 1, we have x = 6 - 3 =3When y = 2, we have x = 6 - 6 = 0Thus, we have the following table:\tx30y12\tPlotting the points {tex}A(3,1)\\ and\\ B(0,2){/tex} and drawing a line joining them, we get the graph of the equation x + 3y = 6 as shown in Fig.Graph of the equation {tex}2x - 3y = 12{/tex} :We have,\xa0{tex} 2 x - 3 y = 12 \\Rightarrow y = \\frac { 2 x - 12 } { 3 }{/tex}When x=3, we have\xa0{tex}y = \\frac { 2 \\times 3 - 12 } { 3 } = - 2{/tex}When x=0, we have\xa0{tex}y = \\frac { 0 - 12 } { 3 } = - 4{/tex}\tx30y-2-4\tPlotting the points {tex}C(3,-2)\\ and\\ D(0, - 4){/tex} on the same graph paper and drawing a line joining them, we obtain the graph of the equation {tex}2x - 3y = 12{/tex} as shown in Fig.Clearly, two lines intersect at P(6, 0).Hence, {tex}x = 6, y = 0{/tex} is the solution of the given system of equations.Putting x = 6, y = 0 in {tex}a = 4x + 3y{/tex}, we geta = (4 {tex}\\times{/tex}\xa06) + (3 {tex}\\times{/tex}\xa00) = 24 | |