Question

solve graphically X-2Y=5,2X+Y=5
please give answer fast​

Answer 1

$\large\underline{\sf{Solution-}}$

↝The given equation of lines are

$\: \: \: \: \: \: \: \: \bull \sf \: x - 2y = 5 - - - (1)$

and

$\: \: \: \: \: \: \: \: \bull \sf \: 2x + y = 5 - - - (2)$

↝ Consider first equation of line

$\rm :\longmapsto\:x - 2y = 5$

1. Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:x - 2 \times 0 = 5$

$\rm :\longmapsto\:x - 0 = 5$

$\bf\implies \:x \: = \: 5$

2. Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:0 - 2y = 5$

$\rm :\longmapsto\: - 2y = 5$

$\bf\implies \:y \: = \: - \: 2.5$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 2.5 \\ \\ \sf 5 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , - 2.5) & (5 , 0)

➢ See the attachment graph. (Purple line)

Now,

↝ Consider Second equation of line,

$\rm :\longmapsto\:2x + y = 5$

1. Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:2 \times 0 + y = 5$

$\rm :\longmapsto\:0 + y = 5$

$\bf\implies \:y \: = \: 5$

2. Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:2x + 0 = 5$

$\rm :\longmapsto\:2x = 5$

$\bf\implies \:x \: = \: 2.5$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 5 \\ \\ \sf 2.5 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 5) & (2.5 , 0)

➢ See the attachment graph. (Blue line)

↝ From graph, we conclude that lines intersecting each other at the point (3, - 1).

$\overbrace{ \underline { \boxed { \bf \therefore\:The\:solution\:is\: x \: = \: 3 \: \: and \: \: y \: = \: - \: 1}}}$