Two rails are represented by the linear equations x + 2y

Q) Two rails are represented by the linear equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0. Represent this situation geometrically.

Ans:

Step 1: Let’s try to find the intersection points on X – axis and Y – axis for each of the lines:

A. For linear equation x + 2 y – 4 = 0:

For X – axis: y = 0

∴ x = 4 – 2 y

= 4 – 2 x 0 = 4

∴ point on X – axis: (4,0)

For Y – axis: x = 0

∴ y = $\frac{4 - x}{2}$

= $\frac {4 - 0}{2}$ = 2

∴ point on Y – axis: (0,2)

B. For linear equation 2 x + 4 y – 12 = 0:

For X – axis: y = 0

∴ x = $\frac{12 - 4 y}{2}$

= 6 – 2 y = 6 – 2 x 0 = 6

∴ point on X – axis: (6,0)

For Y – axis: x = 0

∴ y = $\frac{12 - 2 x}{4}$

= $\frac {6 - x}{2}$ = 3

∴ point on Y – axis: (0,3)

Step 2: To represent the equations graphically, we plot the points P(0,3) and Q (6,0) to get the line PQ.

Similarly, we plot the points R(0,2) and S (4,0) to get the line RS.

Here, the lines do not intersect each other i.e. they are parallel.

Since the rails always run parallel, Therefore, our solution is correct.

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