Chapter 9.7, Problem 7CYU

To determine

Solve the equations.

Answer to Problem 7CYU

  $\left(x,y\right)=\left(5,5\right)$

Explanation of Solution

Given Information: $y=x^2-5x+5$ and $y=5x-20$

Formula Used: Factorization

Calculation:

  $y=x^2-5x+5$ and $y=5x-20$

Now, equate

  $x^2-5x+5=5x-20$

So, simplify

  $x^2-5x+5-5x+20=0$

So,

  $x^2-10x+25=0$

Now, factorize

  $x^2-5x-5x+25=0$

So,

  $x\left(x-5\right)-5\left(x-5\right)=0$

Now,

  $\left(x-5\right)\left(x-5\right)=0$

Hence,

  $x=5$

So, find value of $y$

  $y=5x-20$

Now, put $x=5$

  $y=\left(5\times 5\right)-20$

So,

  $y=25-20$

Hence,

  $y=5$