Question

using the graphical method solve each of the following pairs of simultaneous equation
2x+5y=25
3x-2y=9​

Answer 1

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

Given pair of linear equations are

$\rm :\longmapsto\:2x + 5y = 25$

and

$\rm :\longmapsto\:3x - 2y = 9$

Consider Equation (1)

$\rm :\longmapsto\:2x + 5y = 25$

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

$\rm :\longmapsto\:2 \times 0 + 5y = 25$

$\rm :\longmapsto\: 0 + 5y = 25$

$\rm :\longmapsto\: 5y = 25$

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

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

$\rm :\longmapsto\:2x + 5 \times 0 = 25$

$\rm :\longmapsto\:2x + 0 = 25$

$\rm :\longmapsto\:2x = 25$

$\rm :\longmapsto\:x = 12.5$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 5 \\ \\ \sf 12.5 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.

Consider Equation (2)

$\rm :\longmapsto\:3x - 2y = 9$

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

$\rm :\longmapsto\:3 \times 0 - 2y = 9$

$\rm :\longmapsto\: 0 - 2y = 9$

$\rm :\longmapsto\: - 2y = 9$

$\rm :\longmapsto\: y = - 4.5$

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

$\rm :\longmapsto\:3x - 2 \times 0 = 9$

$\rm :\longmapsto\:3x - 0 = 9$

$\rm :\longmapsto\:3x = 9$

$\rm :\longmapsto\:x = 3$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 4.5 \\ \\ \sf 3 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.

From graph we concluded that

Solution of equations is

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:-\begin{cases} &\sf{x = 5} \\ \\ &\sf{y = 3} \end{cases}\end{gathered}\end{gathered}$