Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

What are the solutions of the system of equations y = –(x 2)2 1 and y = 4x 9? (–2, 1) and (6, –15) (–2, 1) and (–6, –15) (2, 1) and (6, –15) (2, 1) and (–6, –15)

Sagot :

The equations exist [tex]$y =-(x+2)^2+1[/tex] and [tex]y =4x+9[/tex] then the value of

x = -6, x = -2 and y = -15, y = 1.

How to solve the system of equations [tex]$y =-(x+2)^2+1[/tex] and

[tex]y =4x+9[/tex] ?

The given equations are [tex]$y =-(x+2)^2+1[/tex] and [tex]y =4x+9[/tex]

[tex]$-\left(x\:+\:2\right)^2\:+\:1\:=\:4x\:+\:9[/tex]

[tex]$-x^{2}-4 x-3=4 x+9[/tex]

Subtract 9 from both sides, we get

[tex]$-x^{2}-4 x-3-9=4 x+9-9[/tex]

Simplifying the equation, we get

[tex]$-x^{2}-4 x-12=4 x[/tex]

Subtract 4x from both sides

[tex]$-x^{2}-4 x-12-4 x=4 x-4 x[/tex]

[tex]$-x^{2}-8 x-12=0[/tex]

Solve with the quadratic formula

[tex]$x_{1,2}=\frac{-(-8) \pm \sqrt{(-8)^{2}-4(-1)(-12)}}{2(-1)}[/tex]

[tex]$\sqrt{(-8)^{2}-4(-1)(-12)}=4[/tex]

[tex]$x_{1,2}=\frac{-(-8) \pm 4}{2(-1)}[/tex]

Separate the solutions

[tex]$x_{1}=\frac{-(-8)+4}{2(-1)}, x_{2}=\frac{-(-8)-4}{2(-1)}[/tex]

[tex]$x=\frac{-(-8)+4}{2(-1)}=-6[/tex]

[tex]$x=\frac{-(-8)-4}{2(-1)}= \quad-2[/tex]

The solutions to the quadratic equation are x = -6, x = -2

From the above equation [tex]y =4x+9[/tex],

substitute the value of x, then we get

Put, x = -6 then y = 4(-6) + 9 = -15

Put, x = -2 then y = 4(-2) + 9 = 1

The system of equations exists (–2, 1) and (–6, –15).

Therefore, the correct answer is (–2, 1) and (–6, –15).

To learn more about quadratic equations refer to:

https://brainly.com/question/1214333

#SPJ4

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.