# SOLVING WORD PROBLEMS USING GRAPHICAL METHOD

Problem 1 :

Half the perimeter of a rectangular garden, whose length is 4 m more its width is 36 m. Find the dimensions of the garden.

Solution :

Let "x" be the width of the rectangular garden

Let "y" be its length

y = x + 4  -------- (1)

Half the perimeter of the rectangular garden = 36 m

perimeter of rectangle = 2 (L + b)

L + b = 36

y + x = 36

y = 36 - x -------- (2)

Now let us find x and y intercepts to draw the graph.

Graphing 1st line :

y = x + 4

 x-intercept :put y = 0x + 4  =  0x  =  -4  (-4, 0) y - intercept put x = 0y  =  0 + 4y  =  4(0, 4)

Graphing 2nd line :

y  =  36 - x

 x-intercept :put y = 036 - x  =  0x  =  36(36, 0) y - intercept put x = 0y  =  36 - 0y  =  36(0, 36)

Thew above lines are intersecting at the point (16, 20). So, length of the rectangular garden is 20 m and width of the rectangular garden is 16 m.

Problem 2 :

Given the linear equation 2 x + 3 y - 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:

Solution :

(i) intersecting lines

The condition for intersecting lines is a₁/a₂ ≠ b₁/b₂.

According to the above condition, we have to form an equation.

a1 = 2          b1 = 3            c1 = -8

The values of a₂,b₂ and c₂ be any real values but the simplified values of a₁/a₂ and b₁/b₂ shouldn't be equal.

a2 = 3         b2 = -3            c2 = -16

So,  one of the required possible equation is

3x - 3y - 16 = 0.

(ii) Parallel lines

The condition  for two parallel lines is a₁/a₂ = b₁/b₂ ≠ c₁/c₂. According to the above condition, we have to form a equation.

a1 = 2          b1 = 3            c1 = -8

if the value of a₂ is 4, the value of b₂ will be 6. The value of c₂ must be any value other than -16.

a2 = 4         b2 = 6            c2 = 6

So one of the required possible equation is

4x + 6y - 6 = 0.

(iii) Coincident lines

The condition  for coincident lines is a₁/a₂ = b₁/b₂ = c₁/c₂.According to the above condition,we have to form a equation.

a1 = 2          b1 = 3            c1 = -8

the values of a₂, b₂ and c₂ will be

a2 = 4         b2 = 6            c2 = -16

So one of the required possible  equation is

4x + 6y - 16 = 0.

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