Name: Practical Application of Equation and Its Solution
Uploaded: 2019-07-19
Duration: 3 min 8 s
Description: After all the fuss of writing and solving algebraic equations, do you think we will use them in our life? Here are real-life problems that can be solved usin...

Question

The path of a train

A

is given by the equation

2 x - 3 y = 17

and path of another train

B

is given by the linear equation

4 x - 6 y = 18

. Represent the above situations graphically and write your observation.

Accepted Answer

Given, the path of a train $A$ is given by the equation $2 x - 3 y = 17$

The Path of another train $B$ is given by the linear equation $4 x - 6 y = 18$

Both equations represent the linear equation in two variables.

Now we need to draw the graph for the linear equation in two variables.

First we need to express the linear equation in two variables $2 x - 3 y = 17$ and $4 x - 6 y = 18$ in terms of $x$

$\Rightarrow 3 y = 2 x - 17$

$y = \frac{2 x - 17}{3}$

$4 x - 6 y = 18$

$\Rightarrow y = \frac{4 x - 18}{6}$

In order to draw their graph, we need to put different values for $x$ and find the corresponding values for $y$

Then we need to form a table by writing the values of $y$ below the corresponding values of $x$

Table for the equation $y = \frac{2 x - 17}{3}$ is shown as below:

$x$ $1$ $4$ $- 2$

$y$ $- 5$ $- 3$ $- 7$

Now we need to draw a table for the equation $y = \frac{4 x - 18}{6}$

$x$ $0$ $3$ $6$

$y$ $- 3$ $- 1$ $1$

Then draw the coordinate axes on a graph paper and take a suitable scale to plot the points, $(x_{1}, y_{1}), (x_{2}, y_{2})$ ,... on a graph paper.

Join these points $(x_{1}, y_{1}), (x_{2}, y_{2}), . . . .$

We observe that the two equations are represented by two parallel lines. So, we can conclude that trains are moving by maintaining a constant distance between them.

The path of a train $A$ is given by the equation $2 x - 3 y = 17$ and path of another train $B$ is given by the linear equation $4 x - 6 y = 18$ . Represent the above situations graphically and write your observation.

Important Questions on Linear Equations in Two Variables

Learn and Prepare for any exam you want !

The path of a train A is given by the equation 2x-3y=17 and path of another train B is given by the linear equation 4x-6y=18. Represent the above situations graphically and write your observation.

Important Questions on Linear Equations in Two Variables

Learn and Prepare for any exam you want !

The path of a train $A$ is given by the equation $2 x - 3 y = 17$ and path of another train $B$ is given by the linear equation $4 x - 6 y = 18$ . Represent the above situations graphically and write your observation.