Beginning Activity 2: Linear Equations in Two Variables

Beginning Activity Beginning Activity 2: Linear Equations in Two Variables
A4 US

1.

Find integers $x$ and $y$ so that $2 x + 6 y = 25$ or explain why it is not possible to find such a pair of integers.

2.

Find integers $x$ and $y$ so that $6 x - 9 y = 100$ or explain why it is not possible to find such a pair of integers.

3.

Notice that $x = 2$ and $y = 1$ is a solution of the equation $3 x + 5 y = 11,$ and that $x = 7$ and $y = - 2$ is also a solution of the equation $3 x + 5 y = 11 .$

(a)

Find two pairs of integers $x$ and $y$ so that $x > 7$ and $3 x + 5 y = 11 .$ (Try to keep the integer values of $x$ as small as possible.)

(b)

Find two pairs of integers $x$ and $y$ so that $x < 2$ and $3 x + 5 y = 11 .$ (Try to keep the integer values of $x$ as close to 2 as possible.)

(c)

Determine formulas (one for $x$ and one for $y$ ) that will generate pairs of integers $x$ and $y$ so that $3 x + 5 y = 11 .$

Hint.

The two formulas can be written in the form $x = 2 + k m$ and $y = 1 + k n,$ where $k$ is an arbitrary integer and $m$ and $n$ are specific integers.

4.

Notice that $x = 4$ and $y = 0$ is a solution of the equation $4 x + 6 y = 16,$ and that $x = 7$ and $y = - 2$ is a solution of the equation $4 x + 6 y = 16 .$

(a)

Find two pairs of integers $x$ and $y$ so that $x > 7$ and $4 x + 6 y = 16 .$ (Try to keep the integer values of $x$ as small as possible.)

(b)

Find two pairs of integers $x$ and $y$ so that $x < 4$ and $4 x + 6 y = 16 .$ (Try to keep the integer values of $x$ as close to 4 as possible.)

(c)

Determine formulas (one for $x$ and one for $y$ ) that will generate pairs of integers $x$ and $y$ so that $4 x + 6 y = 16 .$

Hint.

The two formulas can be written in the form $x = 4 + k m$ and $y = 0 + k n,$ where $k$ is an arbitrary integer and $m$ and $n$ are specific integers.

Mathematical Reasoning: Writing and Proof (PreTeXt Edition)

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Beginning Activity Beginning Activity 2: Linear Equations in Two Variables
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Beginning Activity Beginning Activity 2: Linear Equations in Two Variables
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