Worksheet: Solving Linear Systems in Word Problems with Matrix Equations

In this worksheet, we will practice solving a system of two linear equations using matrices to solve real-world problems.

Q1:

The length of a rectangle is 6 cm more than twice its width, and twice its length is 39 cm more than its width. Given this, use matrices to determine the perimeter of the rectangle.

Q2:

Half the difference between two numbers is 1, and the sum of the greater number and double the smaller number is 20. Use matrices to find the two numbers.

  • A The numbers are 8 and 6 .
  • B The numbers are 24 and 18.
  • C The numbers are 10 and 11.
  • D The numbers are 8 and 6.
  • E The numbers are 16 and 2.

Q3:

The straight line whose equation is 𝑦 + 𝑎 𝑥 = 𝑐 passes through the two points ( 5 , 5 ) and ( 3 , 1 0 ) . Using matrices, find 𝑎 and 𝑐 .

  • A 𝑎 = 5 , 𝑐 = 6 5
  • B 𝑎 = 1 0 , 𝑐 = 4 5
  • C 𝑎 = 1 5 8 , 𝑐 = 3 5 8
  • D 𝑎 = 5 8 , 𝑐 = 6 5 8
  • E 𝑎 = 3 , 𝑐 = 1 9

Q4:

Mariam and Rania went to Cairo International Book Fair. Mariam bought 10 science books and 7 history books and paid 401 LE, while Rania bought 10 science books and 8 history books and paid 434 LE. Given that all the history books had the same price and all the science books had the same price, use matrices to find the price of a science book and the price of a history book.

  • AEach science book costs 14 LE and each history book costs 37.30 LE.
  • BEach science book costs 33 LE and each history book costs 17 LE.
  • CEach science book costs 7.40 LE and each history book costs 45 LE.
  • DEach science book costs 17 LE and each history book costs 33 LE.

Q5:

A girl bought 37 kilograms of flour and 4 kilograms of butter for 340 LE, and her friend bought 13 kg of flour and 12 kg of butter for 236 LE. Using matrices, find the price per kilogram of both flour and butter.

  • AA kilogram of flour costs 35 LE and a kilogram of butter costs 239 LE.
  • BA kilogram of flour costs 11 LE and a kilogram of butter costs 8 LE.
  • CA kilogram of flour costs 22 LE and a kilogram of butter costs 43 LE.
  • DA kilogram of flour costs 8 LE and a kilogram of butter costs 11 LE.

Q6:

Use matrices to find the two numbers whose sum is 8 and whose difference is 10.

  • A 9 , 1
  • B 1 8 , 2
  • C18, 2
  • D9, 1

Q7:

A motorist paid 190 pounds for 83 litres of petrol and 6 litres of oil. A motorcyclist paid 124 pounds for 22 litres of petrol and 20 litres of oil. Use matrices to find the price per litre of the petrol and the oil, given that the motorist and motorcyclist paid the same price per litre for each.

  • AThe gasoline costs 3 pounds per litre, and the oil costs 4 pounds per litre.
  • BThe gasoline costs 1.75 pounds per litre, and the oil costs 3.50 pounds per litre.
  • CThe gasoline costs 2 pounds per litre, and the oil costs 9.50 pounds per litre.
  • DThe gasoline costs 2 pounds per litre, and the oil costs 4 pounds per litre.

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