Linear relations

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1234System of equations

Solutions to the exercises

Exercise 1

$x = 3 \frac{3}{5}$ and $y = 2 \frac{2}{5}$

$x = 2 \frac{14}{17}$ and $y = \frac{2}{17}$

$x = - \frac{3}{2}$ and $y = \frac{5}{2}$

$x = 10.5$ and $y = 8$ or $x = 4$ and $y = 21$

$x = -3$ and $y = 9$ or $x = 2$ and $y = 4$

$x = \sqrt{5}$ and $y = 2 \sqrt{5}$ or $x = - \sqrt{5}$ and $y = - 2 \sqrt{5}$

Exercise 2

$l \cdot b = 200$ and $2 l + 2 b = 90$ , or $b = 45 - l$ .
Substitution gives you $l (45 - l) = 200$ and this results in $l = 5 \lor l = 40$ .
The rectangle has dimensions of $5$ by $40$ .

Exercise 3

kg cheese = $k$ and kg butter = $b$ .
Then $9.8 k + 22.5 b = 1000$ and $2 k = b$ , therefore $9.8 k + 22.5 \cdot 2 k = 1000$ . This gives you $k = 18.25$ and $b = 36.5$ .

Exercise 4

Take $t$ to be the price of a thuja and $j$ to be the price of a juniper.
Then $20 t + 12 j = 267$ and $2 j + 18 = 5 t$ , or $2 j = 5 t - 18$ .
Substitution: $20 t + 6 (5 t - 18) = 267$ and this gives you $t = 7.5$ and $j = 9.75$ .

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