Chapter 9.7, Problem 35PFA

To determine

Solve the equations.

Answer to Problem 35PFA

Option A and Option B

  $\left(x,y\right)=\left(-1,6\right),\left(-4,0\right)$

Explanation of Solution

Given Information: $y=x^2+7x+12$ and $y=2x+8$

Formula Used: Factorization

Calculation:

  $y=x^2+7x+12$ and $y=2x+8$

Now, equate

  $x^2+7x+12=2x+8$

So, simplify

  $x^2+5x+4=0$

Now, factorize

  $x^2+x+4x+4=0$

So,

  $x\left(x+1\right)+4\left(x+1\right)=0$

Now,

  $\left(x+1\right)\left(x+4\right)=0$

Hence,

  $x=-1$ or $x=-4$

So, find value of $y$

  $y=x^2+7x+12$ or $y=2x+8$

Now, put $x=-1$ or $x=-4$

  $y={\left(-1\right)}^2+7\times \left(-1\right)+12$ or $y=2\times \left(-4\right)+8$

Hence,

  $y=6$ or $y=0$

So, $\left(x,y\right)=\left(-1,6\right),\left(-4,0\right)$