Question

Please help me with this problem to better understandThis system has one solution.{y=−2^x+4y=x2+4x+13 What is the y-coordinate of the solution?Enter your answer in the box.y =

Answer 1

Given:

`\begin{gathered} y=-2x+4\ldots\ldots\ldots\ldots\ldots(1) \\ y=x^2+4x+13\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}`

To find: The y-coordinate of the solution

Step-by-step explanation:

Substituting equation (1) in equation (2) and solving, we get

`\begin{gathered} -2x+4=x^2+4x+13 \\ x^2+4x+13+2x-4=0 \\ x^2+6x+9=0 \\ (x+3)(x+3)=0 \\ x=-3,-3 \end{gathered}`

Substitute the x-value in equation (1) we get,

`\begin{gathered} y=-2(-3)+4 \\ y=6+4 \\ y=10 \end{gathered}`

Thus, the solution is ( -3, 10).

Final answer:

The y-coordinate of the solution is 10.