Question

solve graphically 2x+3y=8; x-2y+3 =0​

Answer 1

Answer:

(1,2) is the solution for the given pair of linear equations

Answer 2

$Given \: Linear \:pair \:of \: equations :$

$2x+3y = 8 \: --(1)$

$\begin {tabular}{|c|c|c|}\cline{1-3} x&-2&4\\\cline{1-3} y&4&0\\\cline{1-3} (x,y)&A(-2,4)&B(4,0)\\\cline{1-3} \end {tabular}$

$and \: x - 2y + 3 = 0 \: --(2)$

$\begin {tabular}{|c|c|c|}\cline{1-3} x&-1&3\\\cline{1-3} y&-2&0\\\cline{1-3} (x,y)&C(-1,-2)&D(3,0)\\\cline{1-3} \end {tabular}$

Now , Plotting the points A,B on the graph and joining them we get a straight line .

And , Plotting the points C,D on the graph and joining them we get another straight line .

These two straight lines intersect at point P.

Finding Coordinates of point P :

$2x + 3y = 8 \: --(1)$

$and \: x = 3 + 2y \: ---(2)$

/* Put x = 3 + 2y in equation (1) , we get */

$2(3+2y) + 3y = 8$

$\implies 6 + 4y + 3y = 8$

$\implies 7y = 8 - 6$

$\implies y = \frac{2}{7}$

$Now , value \: of \: y \: in /:equation \: (2) , we \:get$

$x = 3 + 2 \times \frac{2}{7}$

$\implies x = \frac{21+4}{7}$

$\implies x = \frac{25}{7}$

$\red{Required \: Solution }$

$\green { = P\Big(\frac{25}{7} , \frac{2}{7}\Big)$

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