# Word Problems on System of Linear Equations

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We have also discussed about system of linear equations with elimination and substitution method.

Now let us see how to solve word problems on system of linear equations.

*Example: *The sum of two numbers is 139 while their difference is 19. What is the larger of two numbers?

Let the two numbers be x and y.

*x* + *y* = 139 … Equation (1)

*x* – *y *= 19 … Equation (2)

Adding the two equations, we get,

2x = 139 + 19 ⇒ 2*x* = 158

*x* = 158 ÷ 2 = 79

Put this value of *x* in any of the two equations. Let us put in equation 1:

79 + *y* = 139 ⇒ *y* = 60

Of the two numbers **79** is the larger number.

*Example:* The sum of the digits of a two-digit number is 16. If 18 is added to the number, its digits are interchanged. What is the number?

Let the unit’s digit of the number be *x*.

Ten’s digit = 16 – *x*

Number = 10 × (16 – *x*) + *x* = 160 – 9*x*

When the digits are interchanged, number = 10*x* + (16 – *x*) = 9*x* + 16

160 – 9*x* + 18 = 9*x* + 16

*x* = 9

Ten’s digit = 16 – 9 = 7

Number = **79**

- Twice a number exceeds three times another number by 6. The difference between the numbers is 7. What is the greater of the numbers?
- The perimeter of a rectangular field is 240 m. If length of the field is increased by 8 m and width is decreased by 5 m, the area of the field is decreased by 42 sq m. What is the width of the field?
- The sum of two numbers is 112. When the larger number is divided by the smaller number, the quotient is 5 and the remainder is 4. What is the smaller of the two numbers?
- The tens digit of a two digit number is three times the units digit. The sum of the number and the units digit is 32. Find the number.
- The sum of two digits in a two-digit number is 7. When the digits are interchanged the number is reduced by 9. What is the number?

##### Answer key

- 15
- 46 meters
- 18
- 31
- 43

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