Given:
[tex]\begin{gathered} y=-2x+4\ldots\ldots\ldots\ldots\ldots(1) \\ y=x^2+4x+13\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]
To find: The y-coordinate of the solution
Explanation:
Substituting equation (1) in equation (2) and solving, we get
[tex]\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}[/tex]
Substitute the x-value in equation (1) we get,
[tex]\begin{gathered} y=-2(-3)+4 \\ y=6+4 \\ y=10 \end{gathered}[/tex]
Thus, the solution is ( -3, 10).
Final answer:
The y-coordinate of the solution is 10.
