Questions: Find the missing coordinates to complete the following ordered-pair solutions to the given linear equation y+3x=6 (a) (-1, (b) (5,

Solution Steps

To find the missing coordinates for the ordered-pair solutions to the linear equation \( y + 3x = 6 \), we need to substitute the given x-values into the equation and solve for y. This will give us the complete ordered pairs.

To find the corresponding \( y \) value for the ordered pair when \( x = -1 \), we substitute into the equation \( y + 3x = 6 \):

\[ y + 3(-1) = 6 \]

This simplifies to:

\[ y - 3 = 6 \]

Adding 3 to both sides gives:

\[ y = 9 \]

Thus, the ordered pair is \( (-1, 9) \).

Next, we find the corresponding \( y \) value for the ordered pair when \( x = 5 \) by substituting into the same equation:

\[ y + 3(5) = 6 \]

This simplifies to:

\[ y + 15 = 6 \]

Subtracting 15 from both sides results in:

\[ y = -9 \]

Thus, the ordered pair is \( (5, -9) \).

Final Answer