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 =[]

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

  Answer:

  The y-coordinate of the solution is, 10

  Step-by-step explanation:

  Given the system of equation:

  [tex]y = -2x+4[/tex]            ....[1]

  [tex]y=x^2+4x+13[/tex]         ....[2]

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

  [tex]-2x+4 = x^2+4x+13[/tex]

  Add 2x to both sides of an equation:

  [tex]4 = x^2+6x+13[/tex]

  Subtract 4 from both sides we have;

  [tex]0= x^2+6x+9[/tex]

  or

  [tex]x^2+6x+9=0[/tex]

  Using perfect square:

  [tex](x+a)^2 = x^2+2ax+a^2[/tex]

  ⇒We can write the equation as:

  [tex]x^2+2 \cdot 3x+3^2=0[/tex]

  then;

  [tex](x+3)^2 = 0[/tex]

  ⇒[tex]x+3 = 0[/tex]

  Subtract 3 from both sides we have;

  x = -3

  Substitute value of x in [1] we have;

  [tex]y = -2(-3)+4[/tex]

  ⇒[tex]y =6+4=10[/tex]

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

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