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| 1. |
2x +3y =8 |
| Answer» On a graph paper, draw a horizontal line X\'OX and a vertical line YOY\' as the x-axis and the y-axis respectively.Graph of {tex}2x + 3y = 8{/tex}{tex}2x + 3y = 8{/tex}{tex}\\Rightarrow{/tex}\xa0y = {tex}\\frac{8 - 2x}{3}{/tex}. ...(i)Thus, we have the following table for {tex}2x + 3y = 8{/tex}\tx{tex}1{/tex}{tex}-5{/tex}{tex}7{/tex}y{tex}2{/tex}{tex}6{/tex}{tex}-2{/tex}\tNow, plot the points{tex} A (1, 2), B(-5, 6)\\ and\\ C(7, -2){/tex} on the graph paper.Join AB and AC to get the graph line BC.Thus, the line AC is the graph of the equation {tex}2x + 3y = 8{/tex}.Graph of {tex}x - 2y + 3 = 0{/tex}{tex}x - 2y + 3 = 0{/tex}{tex}\\Rightarrow y = \\frac { x +3 } {2 }{/tex}........(ii)Thus, we have the following table for {tex}x - 2y + 3 = 0\xa0{/tex}\tx{tex}1{/tex}{tex}3{/tex}{tex}-3{/tex}y{tex}2{/tex}{tex}3{/tex}{tex}0{/tex}\tNow, plot the points {tex}P(3,3)\\ and\\ Q (-3, 0){/tex} on the same graph paper.The point {tex}A(1,2){/tex} has already been plotted.Join PA\xa0and QA\xa0to obtain the line PQ.Thus, the line PQ is the graph of the equation {tex}x - 2y + 3 = 0{/tex}Two graphs lines intersect at the point {tex}A(1,2){/tex}{tex}\\therefore{/tex}\xa0{tex}x = 1, y = 2{/tex}\xa0is the solution of the given system of equations. | |