Question

module 11 (linear equations) assignment
score: 10.75/20 answered: 10/20
question 11
find four ordered pair solutions to the given equation by completing the table.
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$$\begin{tabular}{|c|c|} \\hline $x$ & $y = -4x + 2$ \\\\ \\hline 0 & \\\\ \\hline & -6 \\\\ \\hline 5 & \\\\ \\hline & -34 \\\\ \\hline \\end{tabular}$$

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Explanation:

Step1: Find y when x = 0

Substitute \( x = 0 \) into \( y = -4x + 2 \).
\( y = -4(0) + 2 = 0 + 2 = 2 \)

Step2: Find x when y = -6

Substitute \( y = -6 \) into \( y = -4x + 2 \) and solve for \( x \).
\( -6 = -4x + 2 \)
Subtract 2 from both sides: \( -6 - 2 = -4x \)
\( -8 = -4x \)
Divide both sides by -4: \( x = \frac{-8}{-4} = 2 \)

Step3: Find y when x = 5

Substitute \( x = 5 \) into \( y = -4x + 2 \).
\( y = -4(5) + 2 = -20 + 2 = -18 \)

Step4: Find x when y = -34

Substitute \( y = -34 \) into \( y = -4x + 2 \) and solve for \( x \).
\( -34 = -4x + 2 \)
Subtract 2 from both sides: \( -34 - 2 = -4x \)
\( -36 = -4x \)
Divide both sides by -4: \( x = \frac{-36}{-4} = 9 \)

Answer:

The completed table (ordered pairs) is:

• When \( x = 0 \), \( y = 2 \) → \( (0, 2) \)
• When \( y = -6 \), \( x = 2 \) → \( (2, -6) \)
• When \( x = 5 \), \( y = -18 \) → \( (5, -18) \)
• When \( y = -34 \), \( x = 9 \) → \( (9, -34) \)

So the four ordered pair solutions are \((0, 2)\), \((2, -6)\), \((5, -18)\), and \((9, -34)\).