Question

module 11 (linear equations) assignment
score: 10/20 answered: 10/20
question 11
find four ordered pair solutions to the given equation by completing the table.
\

$$\begin{array}{|c|c|} \\hline x & y = -5x - 4 \\\\ \\hline 0 & \\\\ \\hline & -19 \\\\ \\hline 6 & \\\\ \\hline & 44 \\\\ \\hline\\end{array}$$

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Explanation:

Step1: Find y when x = 0

Substitute \( x = 0 \) into \( y = -5x - 4 \).
\( y = -5(0) - 4 = -4 \)

Step2: Find x when y = -19

Substitute \( y = -19 \) into \( y = -5x - 4 \) and solve for \( x \).
\( -19 = -5x - 4 \)
Add 4 to both sides: \( -19 + 4 = -5x \)
\( -15 = -5x \)
Divide by -5: \( x = \frac{-15}{-5} = 3 \)

Step3: Find y when x = 6

Substitute \( x = 6 \) into \( y = -5x - 4 \).
\( y = -5(6) - 4 = -30 - 4 = -34 \)

Step4: Find x when y = 44

Substitute \( y = 44 \) into \( y = -5x - 4 \) and solve for \( x \).
\( 44 = -5x - 4 \)
Add 4 to both sides: \( 44 + 4 = -5x \)
\( 48 = -5x \)
Divide by -5: \( x = \frac{48}{-5} = -9.6 \) (Wait, let's check again. Wait, maybe I made a mistake. Wait, \( y = -5x -4 \), so \( 44 = -5x -4 \) → \( 44 +4 = -5x \) → \( 48 = -5x \) → \( x = -48/5 = -9.6 \)? Wait, no, wait, maybe the equation is \( y = -5x + 4 \)? Wait, the original equation is \( y = -5x -4 \)? Wait, let's re - check. If \( y = 44 \), then \( 44 = -5x -4 \) → \( 5x = -4 -44 \) → \( 5x = -48 \) → \( x = -48/5 = -9.6 \). But maybe the equation was written wrong? Wait, no, the user wrote \( y = -5x -4 \).

Wait, let's redo step 4:

\( y = -5x -4 \)

\( 44 = -5x -4 \)

Add 4 to both sides: \( 44 + 4=-5x \)

\( 48=-5x \)

\( x=\frac{48}{-5}=-9.6 \)

Answer:

When \( x = 0 \), \( y=-4 \); when \( y = - 19 \), \( x = 3 \); when \( x = 6 \), \( y=-34 \); when \( y = 44 \), \( x=-9.6 \)

So the completed table values are:

For \( x = 0 \), \( y=-4 \);

For \( y=-19 \), \( x = 3 \);

For \( x = 6 \), \( y=-34 \);

For \( y = 44 \), \( x=-9.6 \)