Question

1
$y = x + 6$
$y = -2x - 3$
$x + 6 = -2x - 3 - x$
$-x$
$0 = -2x - 5 - x$
$(-3, 3)$

Explanation:

Step1: Set the equations equal

Since \( y = x + 6 \) and \( y = -2x - 3 \), we can set \( x + 6=-2x - 3 \) (the original work had an error here, it should not subtract \( x \) on the right yet).

Step2: Solve for \( x \)

Add \( 2x \) to both sides: \( x + 2x+ 6=-2x+ 2x - 3 \), which simplifies to \( 3x + 6=- 3 \). Then subtract 6 from both sides: \( 3x+6 - 6=-3 - 6 \), so \( 3x=-9 \). Divide by 3: \( x = - 3 \).

Step3: Find \( y \)

Substitute \( x=-3 \) into \( y = x + 6 \): \( y=-3 + 6 = 3 \).

Answer:

The solution to the system of equations \(

$$\begin{cases}y = x + 6\\y=-2x - 3\end{cases}$$

\) is \( x=-3 \), \( y = 3 \) or the ordered pair \( (-3,3) \).