Question

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$$\begin{cases} x = y + 3 \\\\ x = -2y + 12 \\end{cases}$$

Explanation:

Step1: Set the two equations equal

Since both expressions equal \( x \), we can set them equal to each other: \( y + 3=-2y + 12 \)

Step2: Solve for \( y \)

Add \( 2y \) to both sides: \( 3y+3 = 12 \)
Subtract 3 from both sides: \( 3y=9 \)
Divide by 3: \( y = 3 \)

Step3: Solve for \( x \)

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

Answer:

The solution to the system is \( x = 6 \), \( y = 3 \)