Question

Two rails are represented by the equations x+2y-4=0 and 2x+4y-12=0.Represent this algebraically.

Answer 1

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

Given pair of linear equations are

$\rm :\longmapsto\:x + 2y - 4 = 0 - - - (1)$

and

$\rm :\longmapsto\:2x + 4y - 12 = 0 - - - (2)$

Let we plot the lines on graph paper.

Consider Line (1)

$\rm :\longmapsto\:x + 2y - 4 = 0$

can be rewritten as

$\rm :\longmapsto\:x + 2y = 4$

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

$\rm :\longmapsto\:0 + 2y = 4$

$\rm :\longmapsto\:2y = 4$

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

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

$\rm :\longmapsto\:x + 2(0) = 4$

$\rm :\longmapsto\:x + 0 = 4$

$\rm :\longmapsto\:x = 4$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 2 \\ \\ \sf 4 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 2) & (4 , 0)

➢ See the attachment graph.

Now,

Consider Line (2)

$\rm :\longmapsto\:2x + 4y - 12 = 0$

can be rewritten as

$\rm :\longmapsto\:x + 2y = 6$

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

$\rm :\longmapsto\:x + 2(0) = 6$

$\rm :\longmapsto\:x +0 = 6$

$\rm :\longmapsto\:x = 6$

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

$\rm :\longmapsto\:0 + 2y = 6$

$\rm :\longmapsto\:2y = 6$

$\rm :\longmapsto\:y = 3$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 3 \\ \\ \sf 6 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 3) & (6 , 0)

➢ See the attachment graph.