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Linear Equations In Two Variables — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsLinear Equations In Two Variables4 Marks
Question
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 the number of skirts is four less than four times the number of pants purchased." Help her friends to find how many pants and skirts Champa bought.
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Answer

Let us denote the number of pants by x and the number of skirts by y. Then the equations formed are: y = 2x - 2 .....(i) y = 4x - 4 .......(ii) The graphs of the equations (i) and (ii) can be drawn by finding two solutions for each of the equations. They are given in the following table.
x
2
0
y = 2x - 2
2
-2
Hence, the graphic representation is as follows.
The two lines intersect at the point (1, 0). So, x = 1, y = 0 is the required solution of the pair of linear equations, i.e., the number of pants she purchased is 1 and she did not buy any skirt.

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