2. $$ \left\{\begin{array}{l}y=17=-x-3 \ y=x^{2}+8\end{array} ight. $$

Question

2. $$ \left\{\begin{array}{l}y=17=-x-3 \ y=x^{2}+8\end{array}ight. $$

UpStudy AI · Accepted Answer

Solve the system of equations $$ y=-x-3,x^{2}+8=y $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}y=-x-3\x^{2}+8=y\end{array}ight.$$
- step1: Substitute the value of $$y:$$
  $$x^{2}+8=-x-3$$
- step2: Move the expression to the left side:
  $$x^{2}+8-\left(-x-3ight)=0$$
- step3: Calculate:
  $$x^{2}+11+x=0$$
- step4: Rewrite in standard form:
  $$x^{2}+x+11=0$$
- step5: Solve using the quadratic formula:
  $$x=\frac{-1\pm \sqrt{1^{2}-4	imes 11}}{2}$$
- step6: Simplify the expression:
  $$x=\frac{-1\pm \sqrt{-43}}{2}$$
- step7: The expression is undefined:
  $$x 
otin \mathbb{R}$$
- step8: The system of equations has no solution in the set of real numbers:
  $$\left(x,yight) 
otin \mathbb{R}^{2}$$
- step9: Alternative Form:
  $$	extrm{No real solution}$$
The system of equations $$ y=-x-3 $$ and $$ x^{2}+8=y $$ does not have any real solutions.
The system of equations has no real solutions.

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Algebra Questions