Chapter 9.7, Problem 6CYU

To determine

Solve the equations.

Answer to Problem 6CYU

  $\left(x,y\right)=\left(1,2\right),\left(-2,5\right)$

Explanation of Solution

Given Information: $y=-x+3$ and $y=x^2+1$

Formula Used: Factorization

Calculation:

  $y=-x+3$ and $y=x^2+1$

Now, equate

  $-x+3=x^2+1$

So, simplify

  $x^2+1+x-3=0$

So,

  $x^2+x-2=0$

Now, factorize

  $x^2+2x-x-2=0$

So,

  $x\left(x+2\right)-1\left(x+2\right)=0$

Now,

  $\left(x-1\right)\left(x+2\right)=0$

Hence,

  $x=1$ or $x=-2$

So, find value of $y$

  $y=-x+3$ or $y=x^2+1$

Now, put $x=1$ or $x=-2$

  $y=-1+3$ or $y={\left(-2\right)}^2+1$

Hence,

  $y=2$ or $y=5$