Question

Write the equation 2x – 4 = 3x + 1 in (i) one variable and (ii) two variables. Also draw it
geometrically.

Answer 1

Given:

The equation 2x - 4 = 3x + 1.

To find:

1. the equation in one variable
2. the equation in two variables

Step-by-step explanation:

(i)

The given equation is 2x - 4 = 3x + 1.

Let 2x = X and 3x = Y. Then we get

X - 4 = Y + 1

or, X - Y = 1 + 4

or, X - Y = 5, where X = 2x, Y = 3x - 1.

This is the required form.

(ii)

The given equation is 2x - 4 = 3x + 1.

Then, 3x - 2x = - 4 - 1

or, x = - 5

This is the required form.

Geometrical representation:

We have found the simplest form: x = - 5, which represents a straight line parallel to the y-axis in the negative quadrant.

[ Refer to the attached. ]