IDNLearn.com is your go-to resource for finding precise and accurate answers. Ask your questions and receive detailed and reliable answers from our experienced and knowledgeable community members.
Sagot :
To solve the system of equations, we will determine the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy both equations:
[tex]\[ \begin{array}{l} y = x^2 + x + 5 \\ y = x + 1 \end{array} \][/tex]
We can set the right-hand sides of the equations equal to each other, as they both equal [tex]\( y \)[/tex]. So, we have:
[tex]\[ x^2 + x + 5 = x + 1 \][/tex]
Next, we will simplify this equation by moving all terms to one side:
[tex]\[ x^2 + x + 5 - x - 1 = 0 \][/tex]
This simplifies to:
[tex]\[ x^2 + 4 = 0 \][/tex]
To solve for [tex]\( x \)[/tex], we subtract 4 from both sides:
[tex]\[ x^2 = -4 \][/tex]
Taking the square root of both sides, we get:
[tex]\[ x = \pm \sqrt{-4} \][/tex]
The square root of [tex]\(-4\)[/tex] is [tex]\( \pm 2i \)[/tex], where [tex]\( i \)[/tex] is the imaginary unit.
Thus, the solutions for [tex]\( x \)[/tex] are:
[tex]\[ x = \pm 2i \][/tex]
Now, we find the corresponding [tex]\( y \)[/tex] values using [tex]\( y = x + 1 \)[/tex]:
For [tex]\( x = 2i \)[/tex]:
[tex]\[ y = 2i + 1 \][/tex]
For [tex]\( x = -2i \)[/tex]:
[tex]\[ y = -2i + 1 \][/tex]
The solutions to the system of equations are the pairs [tex]\((2i, 2i + 1)\)[/tex] and [tex]\((-2i, -2i + 1)\)[/tex].
These do not match any of the given options exactly.
Therefore, the correct answer to the question is:
B no solution
[tex]\[ \begin{array}{l} y = x^2 + x + 5 \\ y = x + 1 \end{array} \][/tex]
We can set the right-hand sides of the equations equal to each other, as they both equal [tex]\( y \)[/tex]. So, we have:
[tex]\[ x^2 + x + 5 = x + 1 \][/tex]
Next, we will simplify this equation by moving all terms to one side:
[tex]\[ x^2 + x + 5 - x - 1 = 0 \][/tex]
This simplifies to:
[tex]\[ x^2 + 4 = 0 \][/tex]
To solve for [tex]\( x \)[/tex], we subtract 4 from both sides:
[tex]\[ x^2 = -4 \][/tex]
Taking the square root of both sides, we get:
[tex]\[ x = \pm \sqrt{-4} \][/tex]
The square root of [tex]\(-4\)[/tex] is [tex]\( \pm 2i \)[/tex], where [tex]\( i \)[/tex] is the imaginary unit.
Thus, the solutions for [tex]\( x \)[/tex] are:
[tex]\[ x = \pm 2i \][/tex]
Now, we find the corresponding [tex]\( y \)[/tex] values using [tex]\( y = x + 1 \)[/tex]:
For [tex]\( x = 2i \)[/tex]:
[tex]\[ y = 2i + 1 \][/tex]
For [tex]\( x = -2i \)[/tex]:
[tex]\[ y = -2i + 1 \][/tex]
The solutions to the system of equations are the pairs [tex]\((2i, 2i + 1)\)[/tex] and [tex]\((-2i, -2i + 1)\)[/tex].
These do not match any of the given options exactly.
Therefore, the correct answer to the question is:
B no solution
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.