Chapter 9.7, Problem 34PFA

To determine

Solve the equations.

Answer to Problem 34PFA

Option A $\left(x,y\right)=\left(-3,-2\right)$

Explanation of Solution

Given Information: $y=x^2+7x+10$ and $y=x+1$

Formula Used: Factorization

Calculation:

  $y=x^2+7x+10$ and $y=x+1$

Now, equate

  $x^2+7x+10=x+1$

So, simplify

  $x^2+6x+9=0$

Now, factorize

  $x^2+3x+3x+9=0$

So,

  $x\left(x+3\right)+3\left(x+3\right)=0$

Now,

  $\left(x+3\right)\left(x+3\right)=0$

Hence,

  $x=-3$ or $x=-3$

So, find value of $y$

  $y=x^2+7x+10$ or $y=x+1$

Now, put $x=-3$ or $x=-3$

  $y={\left(-3\right)}^2+7\times \left(-3\right)+10$ or $y=-3+1$

Hence,

  $y=-2$ or $y=-2$

So, $\left(x,y\right)=\left(-3,-2\right)$