Question

question 4
this system has one solution.
$y = 10x + 8$
$y = x^2 + 6x + 12$
what is the y-coordinate of the solution?

Explanation:

Step1: Set equations equal

Since both equal \( y \), set \( 10x + 8 = x^2 + 6x + 12 \).

Step2: Rearrange to quadratic

Simplify: \( x^2 - 4x + 4 = 0 \).

Step3: Solve quadratic

Factor: \( (x - 2)^2 = 0 \), so \( x = 2 \).

Step4: Find y - coordinate

Substitute \( x = 2 \) into \( y = 10x + 8 \): \( y = 10(2) + 8 = 28 \).

Answer:

28