# SOLVING SYSTEM OF LINEAR EQUATIONS WORD PROBLEMS IN 2 VARIABLES

Solving System of Linear Equations Word Problems in 2 Variables :

In this section, we will see some examples to understand how to solve system of linear equations word problems in 2 variables.

## Substitution Method Word Problems and Answers

Example 1 :

A fraction becomes 9/11,if 2 is added to both numerator and the denominator.  If, 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.

Solution :

Let “x/y” be the required fraction

If 2 is added to both numerator and denominator the fraction becomes 9/11

(x + 2)/(y+2)  =  9/11

11 (x + 2)  =  9 (y + 2)

11 x + 22  =  9 y + 18

11 x – 9 y  =  18 – 22

11 x – 9 y  =  -4   ------ (1)

3 is added to both the numerator and the denominator it becomes 5/6

(x + 3)/(y+3)  =  5/6

6 (x + 3)  =  5 (y + 3)

6 x + 18  =  5 y + 15

6 x – 5 y  =  15 - 18

6 x – 5 y  =  - 3 ------ (2)

(1) ⋅ 5 ==> 55 x – 45 y  =  -20

(2) ⋅ 9 ==> 54 x – 45 y  =  -27

(-)     (+)         (+)

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

x  =  7

By applying the value of x in (1), we get

6(7) – 5 y  =  -3

42 – 5 y  =  -3

-5y  =  -3 – 42

-5 y  =  -45

y  =  45/5

y  =  9

So, the required fraction is 7/9.

Example 2 :

Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

Solution :

Let “x” be the age of Jacob

Let “y” be the age of his son

5 years hence their ages will be

x + 5 and y + 5

x + 5  =  3 (y + 5)

x + 5  =  3 y + 15

x – 3y  =  -5 + 15

x – 3 y  =  10 ------(1)

5 years ago, their ages was

x – 5 and y – 5

x – 5 = 7 (y – 5)

x – 5 = 7 y – 35

x – 7 y = 5 - 35

x – 7 y = -30 ------(2)

(1) - (2)

x – 3 y  =  10

x – 7 y  =  -30

(-)   (+)    (+)

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

4y  =  40  ==>  y = 10

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

x – 7(10) = -30

x – 70 = -30

x = -30 + 70

x = 40

Therefore age of Jacob's son  =  40

Age of Jacob  =  10 After having gone through the stuff given above, we hope that the students would have understood,solving system of linear equations word problems in 2 variables.

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