**Solving Systems of Equations Word Problems by Elimination Method :**

Here we are going to see some example problems of solving linear equations in two variables.

**Question 1 :**

The monthly income of A and B are in the ratio 3:4 and their monthly expenditures are in the ratio 5:7. If each saves ₹ 5,000 per month, find the monthly income of each.

**Solution :**

Let 3x and 4x be the income of persons A and B respectively.

Let 5y and 7y be the expenditures of persons A and B respectively.

3x - 5y = 5000 ------(1)

4x - 7y = 5000 ------(2)

(1) x 7 => 21x - 35y = 35000

(2) x 5=> 20x - 35y = 25000

(-) (+) (-)

-----------------------

x = 10000

Monthly income of A = 3x = 3(10000) = 30000

Monthly income of B = 4x = 4(10000) = 40000

**Question 2 :**

Five years ago, a man was seven times as old as his son, while five year hence, the man will be four times as old as his son. Find their present age.

**Solution :**

Let "x" and "y" be the ages of a man and his son respectively.

Five years age :

Age of man = x - 5

Age of son = y - 5

(x - 5) = 7(y - 5)

x - 5 = 7y - 35

x - 7y = -35 + 5

x - 7y = -30 -----(1)

Five years later :

Age of man = x + 5

Age of son = y + 5

(x + 5) = 4(y + 5)

x + 5 = 4y + 20

x - 4y = 20 - 5

x - 4y = 15 -------(2)

(1) - (2)

x - 7y = -30

x - 4y = 15

(-) (+) (-)

----------------

-3y = -45

y = 15

By applying the value of y in (2), we get

x - 4(15) = 15

x = 15 + 60

x = 75

Hence the age of man is 75 years and age of son is 15 years.

After having gone through the stuff given above, we hope that the students would have understood, "Solving Systems of Equations Word Problems by Elimination Method"

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