Question

solve the following system by graphing.\

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

\use the graphing tool to graph the system.

Explanation:

Step1: Set the two equations equal

Since both equal \( y \), set \( x^2 + 2x + 6 = 2x + 6 \).

Step2: Simplify the equation

Subtract \( 2x + 6 \) from both sides: \( x^2 + 2x + 6 - (2x + 6) = 0 \), which simplifies to \( x^2 = 0 \).

Step3: Solve for \( x \)

Taking the square root of both sides, \( x = 0 \).

Step4: Find \( y \)

Substitute \( x = 0 \) into \( y = 2x + 6 \), so \( y = 2(0) + 6 = 6 \).

Answer:

The solution to the system is \( (0, 6) \)