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Show graphically that the system of equation 3x-y=2,9x-3y=6 |
| Answer» Graph of {tex}3x - y = 2{/tex}:We have, {tex}3x - y = 2\\Rightarrow y = 3x - 2{/tex}When x = 2, we havey = 3 {tex}\\times{/tex}\xa02 - 2 = 4When x = 1, we havey = 3 {tex}\\times{/tex}\xa01 - 2 = 1\xa0\tx21y41\tPlotting the points {tex}A(2, 4)\\ and\\ B(1, 1){/tex} onthe graph paper and drawing a linepassing through A and B, we obtain thegraph of {tex}3x - y = 2{/tex} as shown in Fig.Graph of {tex}9x - 3 y = 6{/tex} :We have, {tex}9x - 3y = 6{/tex}{tex}\\Rightarrow \\quad y = 9 x - 6{/tex}{tex}\\Rightarrow \\quad y = \\frac { 9 x - 6 } { 3 }{/tex}When, x = 0, We\xa0have{tex}y = \\frac { 9 \\times 0 - 6 } { 3 } = - 2{/tex}When x = -1, we have{tex}y = \\frac { 9 \\times - 1 - 6 } { 3 } = - 5{/tex}\tx0-1y-2-5\tPlotting the points {tex}C(0,-2) and D (-1, - 5){/tex} on the graph paper and drawing a line passing through these two points on the same graph paper we obtain the graph of{tex}9x - 3y = 6{/tex}. We find the C and D both lie on the graph of {tex}3x - y = 2{/tex}. Thus, the graphs of the two equations are coincident.\xa0Hence, the system of equations has infinitely many solutions. | |