Form the pair of linear equations in the following problems, and find their solution graphically:Champa went to a 'sale' to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, The number of skirts is two less than twice the number of pants purchased. Also

Given:

The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased.=
To do:

We have to form the pair of linear equations and solve them graphically. Also, we have to find the number of pants and skirts Champa bought.

Solution:

Let the number of pants and skirts Champa bought be $x$ and $y$ respectively.

According to the question,

$y = 2x-2$.....(i)

$y = 4x-4$.....(ii)

To represent the above equations graphically we need at least two solutions for each of the equations.

For equation $y=2x-2$,

If $x=1$ then $y=2(1)-2=2-2=0$

If $x=0$ then $y=2(0)-2=-2$

For equation $y=4x-4$,

If $x=1$ then $y=4(1)-4=4-4=0$

If $x=0$ then $y=4(0)-4=-4$

The above situation can be plotted graphically as below:

The lines AB and CD represent the equations $y=2x-2$ and $y=4x-4$ respectively.

The solution of the above equations is the point of intersection.

Therefore,

Number of pants $x=1$

Number of skirts $y=0$ 

The number of pants and skirts bought by Champa are $1$ and $0$ respectively. 

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Updated on: 10-Oct-2022

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