Question

This system has one solution.

{y=−2x+4y
{=x2+4x+13

What is the y-coordinate of the solution?

Enter your answer in the box. y =[]

Answer 1

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

Answer 2

The y-coordinate of the solution is, 10

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