Question

This system has one solution.

Answer 1

Answer:

The y-coordinate of the solution is, 10

Step-by-step explanation:

Given the system of equation:

$y = -2x+4$            ....[1]

$y=x^2+4x+13$         ....[2]

Equate the equation [1] and [2] we have;

$-2x+4 = x^2+4x+13$

Add 2x to both sides of an equation:

$4 = x^2+6x+13$

Subtract 4 from both sides we have;

$0= x^2+6x+9$

or

$x^2+6x+9=0$

Using perfect square:

$(x+a)^2 = x^2+2ax+a^2$

⇒We can write the equation as:

$x^2+2 \cdot 3x+3^2=0$

then;

$(x+3)^2 = 0$

⇒$x+3 = 0$

Subtract 3 from both sides we have;

x = -3

Substitute value of x in [1] we have;

$y = -2(-3)+4$

⇒$y =6+4=10$

Solution for the given system of equation = (-3, 10)

Therefore, the  y-coordinate of the solution is, 10

Answer 2

Hello there!
I have just taken the test on this answer and I got 10...
I hope this helps!!