Lesson Worksheet: Applications on Systems of Two Linear Equations Mathematics

In this worksheet, we will practice translating a real-life problem into a system of two linear equations and finding its solution.


Find two numbers with a sum of 42 and a difference of 4.

  • A23, 19
  • B14, 28
  • C26, 19
  • D23, 4
  • E46, 19


A man’s age was four times his daughter’s age, 4 years ago. In 5 years, his age will be three times his daughter’s. Find their ages now.

  • A8 years, 72 years
  • B22 years, 72 years
  • C8 years, 76 years
  • D22 years, 76 years


A family are playing on a seesaw at the park. The seesaw is balanced when the father and daughter sit at one end and two brothers sit at the other. The father’s weight is 7 times his daughter’s and the sons have a combined weight of 96 kg. How much does the daughter weigh?


The length of a rectangle is 6 cm more than its width. If its perimeter is 52 cm, what are its dimensions?

  • A20 cm, 10 cm
  • B32 cm, 13 cm
  • C16 cm, 10 cm
  • D16 cm, 22 cm


Find two numbers with a sum of 42 where one number is one-fifth of the other.

  • A8, 42
  • B7, 35
  • C21, 105
  • D14, 70
  • E10, 52


The sum of two numbers is 56. Given that one of the numbers is one seventh of the other, what are the two numbers?

  • A7, 42
  • B8, 56
  • C17, 39
  • D8, 42
  • E7, 49


Some girls and boys attend a club. Six times the number of girls at the club is 33 more than the number of boys, and 3 times the number of girls is 33 less than six times the number of boys. How many girls and how many boys attend the club?

  • Anumber of girls =7, number of boys =26
  • Bnumber of girls =7, number of boys =5
  • Cnumber of girls =7, number of boys =9
  • Dnumber of girls =5, number of boys =27


In a school competition, students score points for completing long and short puzzles. No points are awarded for incomplete puzzles. Osama scored 85 points for completing 4 long and 5 short puzzles, and Abdullah scored 85 points for completing 3 long and 8 short puzzles. How many points did Hassan score for completing 5 long and 5 short puzzles?


When the digits of a two digit number are reversed, the result is 27 more than the original number. If the sum of the digits is 9, what was the original two digit number?


The difference between the measures of the acute angles in a right triangle is 52. Find the measure of each acute angle.

  • A38, 52
  • B19, 52
  • C64, 26
  • D38, 71
  • E19, 71

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