Chapter 9.7, Problem 18PPS

To determine

Solve the equations.

Answer to Problem 18PPS

  $\left(x,y\right)=\left(5,4\right)$

Explanation of Solution

Given Information: $y=x^2-8x+19$ and $x-0.5y=3$

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

Calculation:

  $y=x^2-8x+19$ and $x-0.5y=3$

So,

  $y=x^2-8x+19$ and $x-3=0.5y$

Now,

  $y=x^2-8x+19$ and $y=2x-6$

Now, equate

  $x^2-8x+19=2x-6$

So, simplify

  $x^2-8x+19-2x+6=0$

So,

  $x^2-10x+25=0$

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 $y$

  $y=2x-6$

Now, put $x=5$

  $y=\left(2\times 5\right)-6$

Hence,

  $y=4$