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In this lesson, we will learn how to solve a system of two linear equations using matrices to solve real-world problems.

Q1:

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.

Q2:

The straight line whose equation is π¦ + π π₯ = π passes through the two points ( β 5 , 5 ) and ( 3 , 1 0 ) . Using matrices, find π and π .

Q3:

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.

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.

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.

Q6:

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

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.

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