Question

Write four solutions for each of the following equations: 

(i) 2x + y = 7 

(ii) πx + y = 9 

(iii) x = 4y

Answer 1

Given Equations and their Solutions:

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(i) Equation: \( 2x + y = 7 \)

Let's find four solutions for the given equation.

Solution 1: Let \( x = 0 \)

Substitute \( x = 0 \) into the equation:

\[ 2(0) + y = 7 \Rightarrow y = 7 \] 

So, the first solution is \( (x, y) = (0, 7) \).

Solution 2: Let \( x = 1 \)

Substitute \( x = 1 \) into the equation:

\[ 2(1) + y = 7 \Rightarrow y = 5 \]

So, the second solution is \( (x, y) = (1, 5) \).

Solution 3: Let \( x = 2 \)

Substitute \( x = 2 \) into the equation:

\[ 2(2) + y = 7 \Rightarrow y = 3 \]

So, the third solution is \( (x, y) = (2, 3) \).

Solution 4: Let \( x = 3 \)

Substitute \( x = 3 \) into the equation:

\[ 2(3) + y = 7 \Rightarrow y = 1 \]

So, the fourth solution is \( (x, y) = (3, 1) \).

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(ii) Equation: \( \pi x + y = 9 \)

Let's find four solutions for the given equation.

Solution 1: Let \( x = 0 \)

Substitute \( x = 0 \) into the equation:

\[ \pi(0) + y = 9 \Rightarrow y = 9 \]

So, the first solution is \( (x, y) = (0, 9) \).

Solution 2: Let \( x = 1 \)

Substitute \( x = 1 \) into the equation:

\[ \pi(1) + y = 9 \Rightarrow y = 9 - \pi \approx 9 - 3.1416 = 5.8584 \]

So, the second solution is \( (x, y) = (1, 5.8584) \).

Solution 3: Let \( x = 2 \)

Substitute \( x = 2 \) into the equation:

\[ \pi(2) + y = 9 \Rightarrow y = 9 - 2\pi \approx 9 - 6.2832 = 2.7168 \]

So, the third solution is \( (x, y) = (2, 2.7168) \).

Solution 4: Let \( x = 3 \)

Substitute \( x = 3 \) into the equation:

\[ \pi(3) + y = 9 \Rightarrow y = 9 - 3\pi \approx 9 - 9.4248 = -0.4248 \]

So, the fourth solution is \( (x, y) = (3, -0.4248) \).

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(iii) Equation: \( x = 4y \)

Let's find four solutions for the given equation.

Solution 1: Let \( y = 0 \)

Substitute \( y = 0 \) into the equation:

\[ x = 4(0) \Rightarrow x = 0 \]

So, the first solution is \( (x, y) = (0, 0) \).

Solution 2: Let \( y = 1 \)

Substitute \( y = 1 \) into the equation:

\[ x = 4(1) \Rightarrow x = 4 \]

So, the second solution is \( (x, y) = (4, 1) \).

Solution 3: Let \( y = -1 \)

Substitute \( y = -1 \) into the equation:

\[ x = 4(-1) \Rightarrow x = -4 \]

So, the third solution is \( (x, y) = (-4, -1) \).

Solution 4: Let \( y = 2 \)

Substitute \( y = 2 \) into the equation:

\[ x = 4(2) \Rightarrow x = 8 \]

So, the fourth solution is \( (x, y) = (8, 2) \).