Linear relations

Linear relations > System of equations

Overview

1234System of equations

Exercises

Exercise 1

Solve the following systems of equations:

${\begin{matrix} x + y = 6 \\ 2 x - 3 y = 0 \end{matrix}$

${\begin{matrix} 2 x + 4 y = 7 \\ 3 x + 5 y = 8 \end{matrix}$

${\begin{matrix} y = x^{2} \\ x + y = 6 \end{matrix}$

${\begin{matrix} 4 x + 6 y = 12 \\ 3 x - 4 y = 8 \end{matrix}$

${\begin{matrix} x \cdot y = 84 \\ 2 x + y = 29 \end{matrix}$

${\begin{matrix} x^{2} + y^{2} = 25 \\ y = 2 x \end{matrix}$

Exercise 2

A rectangle has an area of $200$ cm² and a perimeter of $90$ cm. Use $l$ for the length and $b$ for the width of the rectangle, both in cm.

Set up the two equations that apply to $l$ and $b$ . Calculate the solution for this system of equations.

Exercise 3

A dairy uses $9.8$ kg of milk for $1$ kg of full-fat cheese. They need $22.5$ kg milk to make $1$ kg of butter. They have $1000$ kg milk in stock. The dairy always makes twice as much butter as cheese.

How many kg of cheese and how many kg of butter can be made from the available milk stocks? Solve this problem using a system of two equations with two variables.

Exercise 4

Someone buys a number of young evergreen plants for a hedge: $20$ thujas and $12$ junipers. He pays € 267. After planting he is left with $2$ junipers, but he needs another $5$ thujas. At the garden center they are willing to exchange the two junipers for five thujas, but an extra € 18 have to be paid.

How much does a thuja cost, and how much does a juniper cost?

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