Chapter 9.7, Problem 20PPS

To determine

Solve the equations.

Answer to Problem 20PPS

  $\left(x,y\right)=\left(5,5\right)$

Explanation of Solution

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

Formula Used: $a^2-2ab+b^2={\left(a-b\right)}^2$

Calculation:

  $y=5x-20$ and $y=x^2-5x+5$

Now, equate

  $5x-20=x^2-5x+5$

So, simplify

  $$

  $x^2-10x+25=0$

x2−5x+5−5x+20 = 0

So,

Now, Use formula $a^2-2ab+b^2={\left(a-b\right)}^2$

  ${\left(x-5\right)}^2=0$

Now, square root both sides.

  $x-5=0$

Hence,

  $x=5$

So, find value of $y$

  $y=5x-20$

Now, put $x=5$

  $y=\left(5\times 5\right)-20$

Hence,

  $y=5$